1.a Extras and minimal physical duplicates

The blockers problem is targeted at supervenience formulations of physicalism, but it is not aimed at every such formulation. The formulations at issue are those modified in response to a different, preexisting problem for supervenience formulations, one known as the problem of “epiphenomenal ectoplasm” (Stoljar Reference Stoljar2010) or the “problem of extras” (Witmer Reference Witmer1999, Francescotti Reference Francescotti2014).

This problem arises from the apparent contingency of physicalism. One natural approach to characterizing physicalism suggests the following global supervenience thesis:

S is too strong a condition to be necessary for physicalism. It rules out possibilities in which conditions contrary to physicalism are simply added in an idle way to an otherwise purely physical world. Most physicalists hold that the doctrine is a contingent truth; there could have been things of a sort inconsistent with physicalism even if no such things are actual. If those things could simply be tacked on as extras to an otherwise purely physical world, S is false. Yet this possibility does nothing to impugn the physicalist credentials of the world lacking such extras. Physicalism is thus compatible with the falsity of S. Footnote ³

If we want a supervenience thesis that is at least necessary for physicalism, we need something weaker than S. Three well-known proposals for such—due to Frank Jackson (Reference Jackson, O’Leary-Hawthorne and Michael1994, Reference Jackson1998), David Lewis (Reference Lewis1983), and David Chalmers (Reference Chalmers1996)—are examined in Hawthorne’s Reference Hawthorne2002 paper. For reasons of space, I focus exclusively on Jackson’s minimal physical duplicate formulation, hereafter MPD:

A world is a physical duplicate of another iff the two are indiscernible with respect to both the instantiation of physical properties and the laws of physics. It is a minimal physical duplicate of another iff it is a duplicate thereof and contains nothing more than what is needed to attain such indiscernibility. As Jackson likes to put it, if God were to take the physical description of the actual world as a recipe and build a world to those specifications and stop right there, adding no further ingredients, that would be a minimal physical duplicate of the actual world.

The appeal of MPD as a replacement for S is plain: by excluding from consideration those possible worlds in which add-ons exist, it appears to trim off precisely those implications of S that caused trouble. Such worlds seem to be irrelevant to the truth of physicalism, but it is precisely at this point that blockers come into play. In effect, blockers challenge the idea that these nonactual worlds with add-ons are uniformly irrelevant. If the add-on is a blocker of the troublesome sort, then such worlds are relevant after all.

1.b Blockers and relevant worlds

So what exactly is a blocker? Though the term suggests a two-term relation (blocker and blockee), the relation requires three terms: a condition that necessitates some feature unless the blocker is present, in which case that feature may or may not appear. Let us say that B blocks F relative to P and define the relation thus (the modality here is metaphysical necessity and possibility):

Our interest is not in the blocking relation per se but in certain situations in which the relevant kinds of properties stand in that relation. Distinguish three kinds of properties: the physical, the nonphysical, and the contraphysical. As I use nonphysical, calling a property nonphysical only means that it is not initially counted as physical when classifying properties as physical or not; it is not “narrowly” physical but might be “broadly” physical in the sense of being related to the narrowly physical in the way the physicalist thinks all instantiated properties are related to such. By contrast, I will use contraphysical to classify any property that both fails to be physical and is incapable of being related in that way (whatever it is exactly) to the narrowly physical. Blocker properties are going to be contraphysical; in the present discussion, any possible world being evaluated for consistency with physicalism will be one devoid of any instances of a blocker property. The relevance of the blocker property will reside rather in the light it sheds on what is going on in a world where it is not instantiated.

Those worlds may be called blocker-relevant worlds and be defined thus:

Suppose the actual world is a blocker-relevant world in this sense. Any minimal physical duplicate of the actual world will be one without B, since B is a contraphysical property. As a result, anything in that duplicate world that has P will also have F, since P necessitates F so long as B is absent. So far as the pattern of individuals with P having F goes, then, no difference between that minimal physical duplicate and the actual world will show up. There are, then, possible worlds which meet all four conditions of being a blocker-relevant world.

1.c Innocent versus troublesome blockers

The point of blockers is to show that MPD is insufficient for physicalism. If being a blocker-relevant world is itself inconsistent with being a world in which physicalism is true (hereafter, a physicalist world), then, since blocker-relevant worlds are possible, MPD is not sufficient for physicalism. It is plain, however, that being a blocker-relevant world is not inconsistent with being a physicalist world.

Hawthorne makes the point using the example of being a spookless cake, that is, being a cake that is not accompanied by a spook, where being a spook is a contraphysical property. Let C be a physical property that suffices for being a cake. A world in which there are no spooks, everything with C is a cake, and there are spookless cakes may still be a physicalist world. So a world can be blocker-relevant yet still be one in which physicalism is true. Some blockers, then, are “innocent” in the sense that they pose no threat to physicalism.

But there might also, it seems, be “troublesome” blockers. Hawthorne uses the example of pain to prompt the worry. Say that in the actual world, an individual Amy has a bad headache. Let H be the property of having that kind of headache and N be some complex physical (perhaps neurological) property Amy instantiates—one that encompasses whatever physical features a physicalist may think relevant to her having H.Footnote ⁴ If it encompasses all the relevant physical features, a physicalist will presumably say that Amy’s having H is nothing over and above her having N.

But now suppose that there is some contraphysical property B_NH that blocks H relative to N. We are not supposing B_NH is actually instantiated, only that it could be. On the face of it, this possibility disqualifies the actual world from being a physicalist world. Here’s why: from our suppositions, it follows that there is some nonactual world in which someone has both N and B _NH and lacks H. As a result, something could have the physical property N yet still not have H. This certainly looks to be incompatible with the claim that Amy’s having H is nothing over and above her having N.

What makes for the difference between innocent and troublesome blockers? Hawthorne suggests that what matters is whether the blockable property or fact is “positive”:

Later in this paper I will reexamine this way of capturing the innocent/troublesome distinction. But it is not hard to see its initial appeal. In both the pain and spookless cake cases, something about the lack of a contraphysical entity explains a fact about the actual world. But in the innocent case, the fact about the actual world appears distinctively negative itself; as such, it seems appropriate to explain it by reference to another lack. In the troublesome case, however, the fact being explained—that Amy is in pain—does not appear to concern a lack of things, so the role of a contraphysical entity in explaining it raises suspicions about whether the explained fact is itself consistent with physicalism.

Exactly what suspicions are raised and why are questions I reserve until later when the innocent/troublesome distinction is at center stage. For now, let us rely on an intuitive sense of what makes for trouble and introduce a handy abbreviation. Let us say a world is a troublesome blocker-relevant world (or TBR world) iff it is a blocker-relevant world such that something about the conditions that make it a blocker-relevant world also make it a world in which physicalism is false.

2.a Miracles, laws and physical duplicates

Why think any TBR worlds are possible in the first place? How are we to conceive of such a situation? Hawthorne provides a brief suggestion in a footnote:

Call this the supernatural intervention strategy for conceiving of troublesome blockers. As I have defined blockers, they are properties, not individuals as in the passage above, but we can transpose the suggestion and speak of the property of being accompanied by a miracle worker of the relevant sort. Following this suggestion, let us build on our earlier sketch involving Amy and her headache to see if we can add enough details to make for a conceivable TBR world.

Earlier I introduced B_NH as a contraphysical property that blocks H relative to N but did not characterize it any further, leaving it unclear whether we have any idea whether a situation of that sort is possible. But now we have a strategy; let us characterize B_NH as the property of being accompanied by a miracle worker who wills that there be no pain accompanying N. If we grant that miracle workers are possible, then shouldn’t we also grant that the world just described is possible and, hence, that a TBR world is possible?

No. Depending on just what choices we make in trying to fill in the description, we find that the world is either clearly impossible, possible but not troublesome, or dependent on a supposition the possibility of which is itself dubious. To see this, two preliminary points regarding miracles and physical duplicates must be kept firmly in mind.

The first point is familiar. Granting the possibility of supernatural intervention may be admissible, but the miracle worker should not be understood as having the ability to violate metaphysical necessities. Not even God, were he to exist, could do that. The supernatural intervention strategy, then, turns on the implicit idea that the link between N and H is mediated by natural law.Footnote ⁵ Let L_NH be the relevant law, something that at least includes the implication that anything with N must have H as well. In any world in which B_NH is instantiated, then, some miracle worker suspends that law, allowing things with N to fail to have H.

The second point concerns what it takes for one world to be a physical duplicate of another—minimal or otherwise. The two worlds must match with respect to the pattern of instantiation of physical properties, but that is not all: the laws of physics must match as well.Footnote ⁶ One could define a notion of physical duplication—and a corresponding supervenience thesis—that doesn’t require a match in the laws of physics. But the resulting thesis would be obviously too strong a condition on physicalism. Consider a thin and fragile pane of glass in the actual world and another world such that it (i) matches the actual world perfectly with respect to which physical properties are instantiated yet (ii) differs with respect to the laws of physics, specifically in a way that renders the corresponding pane of glass practically unbreakable. The point is just that many of the nonphysical properties we want to ensure appear in the duplicate world depend for their instantiation not only on the actual distribution of physical properties but also on the laws that govern their behavior. Any reasonable proposal to formulate physicalism as a supervenience thesis must, then, include those laws among what must be duplicated. If there are laws of nature other than the laws of physics, they are not automatically duplicated but will be so only if they are necessitated by the conditions that are automatically duplicated—which conditions include the laws of physics themselves.

Now let us return to our attempt to conceive of a TBR world. Let w_A (for Amy) be the candidate TBR world in which Amy has N and H, lacks B_NH , and law L_NH is operative. We suppose there is some distinct possible world w_B (for Blocker) in which the miracle worker exists and suspends L_NH ; there, Amy has N but lacks H. Our situation thus far conceived looks like this:

So far, so good. But all is not well, as we see when we focus on a couple of questions the answers to which have not yet been settled. Whichever way we answer those questions, the resulting description of w_A will not allow us to be confident that it is both possible and a genuine TBR world.

2.c Is the law entailed by the physical laws and conditions?

Our first question concerns how the law L_NH relates to the physical laws and conditions in w_A . That law is presumably not among the laws of physics at w_A given that it governs a nonphysical property, namely, H.Footnote ⁷ Still, it may be related to those physical laws in an important way. The key question is whether, in imagining the case, we should stipulate that the following entailment thesis is true or false.

Suppose we stipulate that it is false. On this option, notably, a minimal physical duplicate of w_A will be one in which L_NH is not a law. After all, such a duplicate will replicate the distribution of physical properties and the laws of physics in w_A and nothing further—unless that something else is necessitated by those two factors. By supposing the entailment thesis false, however, we are supposing L_NH is not so necessitated. Including L_NH would be including an “extra” not properly required by the physical laws and conditions, so no minimal physical duplicate of w_A is one in which L _NH is a law.

What does this mean for Amy and her headache? In w_A , the headache she suffers is a consequence of her instantiating physical property N and the law L_NH . In constructing a minimal physical duplicate of w_A we need to be sure she has N again, but since the law L_NH is not included, there is no requirement that she have H as well. And, again, a minimal physical duplicate excludes everything not required by the duplicated physical conditions, so in any minimal physical duplicate of w_A , Amy is headache free.

This result, however, means that w_A is not a TBR world. Recall that condition (iv) on being a TBR world is that any minimal physical duplicate of the world in question is a duplicate simpliciter. By stipulating the falsity of the entailment thesis above, we ensure that minimal physical duplicates of w_A differ from w_A in that Amy lacks H in those duplicates.

If, then, we want w_A to be a TBR world, we must stipulate that L_NH is indeed necessitated by the physical laws and instances in w_A . With that stipulation, any minimal physical duplicate of w_A will include L_NH as a law and thus ensure that Amy has not only N but H as well, so there is no problem supposing it to be a duplicate simpliciter.

So far, so good. What we’ve said seems to be compatible with there being a nonminimal physical duplicate of w_A, one in which our miracle worker is added, where that miracle worker suspends L_NH and allows Amy to be free of her headache. Another problem comes into view, however, when we think further about how we are to conceive of the miracle working as suspending L_NH on this option.

2.d Is the miraculous action direct or indirect?

There are two importantly different ways we might imagine the miracle working achieving his goal. On one option, the miracle is effected directly: the intervener overrides or suspends the law L_NH without having to change any other laws or conditions. Alternatively, the miracle is effected indirectly: he intervenes by changing some other law and/or conditions. In filling out our picture, which option should we stipulate?

Suppose that the miracle is direct. This is likely the most natural way of imagining the case: we start with a world just like w_A , add the miracle worker, and change the conditions of the world in only one further way: everyone with N simply has his or her headache removed, without changing anything else. The result is a world w_B which is indiscernible from w_A except in those two respects (the presence of the blocker and the removal of those headaches). Notably, however, w_B is still a physical duplicate of w_A : the physical laws and the contingent physical conditions remain a perfect match between the two worlds.

This fact should give us pause. We are presently working under two stipulations: that L _NH is indeed entailed by the laws of physics and physical conditions in w_A and that the miracle is effected directly, so w_B is a possible world. These two stipulations seem to conflict with each other. After all, in w_B the miracle worker has supposedly suspended L_NH even while leaving in place conditions that ensure that L_NH is a law. On the face of it, this is a self-contradiction.

But this complaint is too quick. If we take seriously the possibility of miraculous intervention, we must think there is some coherent account of how something could be a law even while being suspended. And there is such an account. On what I take to be the traditional approach, laws of nature are implicitly conditional, applying only when nothing outside the system interferes with it (Mackie Reference Mackie1982, 19–20). The suspension or violation of the law is understood as its being rendered irrelevant because a requisite background condition is not satisfied.

We should, then, understand the law L_NH as similarly conditional, perhaps having as its content something like this:

This enables us to evade the self-contradiction. We can hold that L_NH is still a law in w_B even though it fails to apply to anything, as everything in that world has B_NH —everything is accompanied by the relevant kind of miracle worker. The physical conditions common to w_A and w_B necessitate that L_NH is a law, but in w_B the miracle worker’s presence ensures that the law has no consequences. Have we now conceived of a TBR world?

Not clearly. We have avoided self-contradiction but at the price of introducing a supposition the possibility of which is itself unclear. Note that the law L_NH is now supposed to have a form like that given above and to be such that the physical conditions and laws common to w_A and w_B necessitate that L_NH is a law. It is hard to see how it could be thus necessitated given that it includes an escape clause referring specifically to this contraphysical property B_NH . Consider by contrast the idea that those physical conditions necessitate that it be a law that anything with N has H. Since H is nonphysical but not contraphysical, it is capable of being related to the physical in the way that physicalism requires; as a result, it doesn’t seem perplexing that physical conditions and laws might entail the law relating N and H. By contrast, B_NH is contraphysical; it is hard to see how purely physical factors could have any nontrivial implications about the conditions under which B_NH is instantiated.Footnote ⁹

There is a subtly different option one might propose. Instead of the escape clause citing some contraphysical condition specifically, the clause might be more general and merely subsume such conditions without being about them. If we say that a law of nature only describes how nature works when nothing outside the system interferes with it, that “nothing outside” clause says nothing about any contraphysical entities as such. Perhaps it is more plausible that purely physical laws and conditions could entail a law with that kind of escape clause.

Still, how is the talk of “interference” to be understood on this approach? The natural approach here is to say that the escape clause is “unless something not itself physical interferes with physical conditions.” After all, those other physical conditions are what otherwise ensure that anything with N has H. If that’s right, however, then what we are imagining is not direct miraculous intervention. It is rather indirect intervention: the contraphysical entity works its magic by first interfering with the physical conditions, which interference results in the inapplicability of L_NH .

So we are now considering the other option on the table: supernatural intervention that works indirectly. Might conceiving of that sort of miracle worker enable us to conceive of a TBR world?

No. The problem this time is different, however. Instead of the candidate world being of dubious possibility, there is nothing in it to threaten the truth of physicalism therein. If a miracle worker had existed and changed the physical conditions on which Amy’s headache depends and thereby took away her headache, this hardly shows that her headache wasn’t dependent on those physical conditions. Indeed, it illustrates that dependence. For all we have said about the case, this dependence may be of the sort required for physicalism.

To fill in the case a bit more, suppose that the headache property is functional in nature and the physical N is, given the laws of physics, sufficient to ensure that the bearer of N has a property that plays that role. Nothing in this case is contrary to physicalism, but it is also consistent with the possibility that some supernatural intervener might change the laws of physics in a way so that N no longer suffices for that role to be played. But this kind of blockability is benign. It is no more contrary to physicalism than the truth of the following counterfactual:

Supposing that magical spirits are at all possible, a physicalist should allow the truth of this counterfactual. (And if they are not possible, or if no supernatural interveners capable of changing physical conditions are possible, this route to a TBR world is blocked anyway.)

Let me sum up our results. The supernatural intervention strategy requires seeing N and H as linked by a law of nature instead of a metaphysically necessary connection. That law is itself either entailed by the laws of physics at w_A or not. If not, then a minimal physical duplicate of w_A is not a duplicate simpliciter, so w_A is not a TBR world. If the law is entailed by those physical laws and conditions, then the action of the supernatural intervener is either direct or indirect. If it is direct, the world we are trying to imagine threatens to be self-contradictory; at best, it is hard to see how the purely physical conditions and laws could necessitate a law with an exception clause specifically about some contraphysical entity. If it is indirect, the world we are trying to imagine is perfectly coherent, but the possibility of that world does not threaten the status of physicalism at w_A . In no case, then, have we clearly conceived of a possible TBR world.

3.a “Positive” facts and properties

Our attempt to conceive clearly of a TBR world has not succeeded. One may suspect that troublesome blockers are just impossible. Before drawing any such conclusion, however, we would do well to try for a better understanding of what makes a blocker-relevant world troublesome in the first place, starting with Hawthorne’s suggestion.

That suggestion seems both appealing and simple: if the blockable fact is a “positive fact,” then its blockability is troublesome. We can represent his suggestion as adding a fifth condition to the four that define a blocker-relevant world. The fifth condition is just:

A TBR world, then, might be a blocker-relevant world that meets not only conditions (i)–(iv) but also condition (v).

Whether we should define TBR worlds in this way depends, obviously, on how “positive fact” is understood. Hawthorne alludes to—without endorsing—the way the term is used by David Chalmers (Reference Chalmers1996, 38–41) when giving his own proposal for a supervenience thesis that allows “extras.”Footnote ¹⁰ There we find the distinction explained as follows:Footnote ¹¹

Suppose we define a TBR world as a world that meets conditions (i)–(v) and understand “positive fact” as defined above by Chalmers. Does this definition better enable us to clearly conceive of troublesome blockers?

Far from making it easier, the definition makes it impossible to conceive of a TBR world. If a positive fact is defined as one that “cannot be negated simply by enlarging a world,” then positive facts are by definition not blockable. On the present suggestion, the blockers problem can be quickly dismissed. Indeed, the dismissal is too quick, suggesting that we have simply failed to diagnose the difference between innocent and troublesome blockers.

But the problem with using (v) to define a TBR world runs deeper yet. Suppose we jettison Chalmers’s modal definition of positive fact and lean instead on some intuitive understanding of positive fact. Arguably, the resulting definition of a TBR world now fails for the opposite reason: instead of rendering such worlds obviously impossible, it will imply that it is too easy for a world to count as TBR.

I say “arguably” because the definition can only be applied by relying on some intuitive notion of positive fact, and I am not sure I have any such notion. But others apparently do. Among them is Stephan Leuenberger, whose judgements concerning which facts count as positive, if accepted, make it too easy for a world to be TBR. I have in mind his review of three examples he brings up in response to what he calls the “unblockability objection”—the claim that “positive facts such as itches and pains … are not blockable, unlike negative facts” (Reference Leuenberger and Zimmerman2008, 152). Against this, he offers three examples of blockable positive facts. Consider just the third of these.

If this fact counts as positive, then the example shows that the definition of a TBR world using (v) is too permissive. If we let the gunk here be contraphysical, the example can meet conditions (i)–(v) yet still be intuitively consistent with physicalism. If we think about what goes into the object’s disposition to reflect photons, the relevant factors resolve themselves into physical factors and an acceptable lack of contraphysical factors. Why does it have the disposition to reflect photons? Part of the answer appeals to the physical features of the object; another part appeals to the fact that nothing would prevent such reflection if the opportunity were to arise. The lack of contraphysical gunk is subsumed under the latter. Compare to the case of a spookless cake. Why is this thing a spookless cake? The factors break into the same two categories: physical facts (making it a cake) and a lack of contraphysical factors (making it spookless). That combination suffices to explain why being a spookless cake is instantiated. Nothing here should make us worry that its instantiation is dependent in an objectionable way on something contraphysical.

If, then, we count this kind of case as a positive fact, then the proposed definition of a TBR world is to be rejected as too inclusive.Footnote ¹² Leuenberger himself should be happy with this result, as his own proposal is to formulate physicalism in a way that admits the possibility of blockers generally—not recognizing any category of troublesome blockers. This is again too quick, in my view; we can identify what makes for a TBR world, though it’s easiest to see how if we drop the attempt to capture the notion using talk of a “positive” fact or property.

3.b Grounds for trouble

In reviewing the disposition case above, I argued that it was no threat to physicalism by appeal to explanation: the factors that explained the object’s possessing the disposition were all factors acceptable to the physicalist: either physical facts or facts about the absence of contraphysical entities. The kind of explanation at issue is that associated with metaphysical grounding: what makes it the case that the object has the disposition, or what grounds the fact that it has the disposition, is the fact that it has such and such physical factors that would cause it under appropriate circumstances to reflect photons. What makes this blocker innocent is, it seems, the fact that the property at issue (having the disposition) is grounded entirely in facts acceptable to the physicalist. Accordingly, we may venture the hypothesis that a troublesome blocker relevant world is one in which the blockable property F is grounded at least in part in something not acceptable for the physicalist.

Whatever that is, it cannot be the fact that something in the world has the contraphysical blocker property—since by hypothesis nothing in that world has that property. Nor can it be the fact that something lacks that property; we can hardly say that physicalism is falsified in this world because something lacks a contraphysical property. Instead, if this diagnosis is on the right track, we must suppose there is some other contraphysical property in the picture, one actually instantiated in the TBR world. Of course, when Hawthorne described the case of blockable pain and created the impression that such a world is contrary to physicalism, he did not describe any contraphysical entity other than the blocker. My suggestion, nonetheless, is that the structure of the example naturally leads us to posit something else contraphysical.

Say we are told only the bare details: Amy has the physical property N and the headache property H; she does not have the blocker property B_NH that blocks H relative to N. We’re also told that a minimal physical duplicate of this world is one in which all three of these facts are replicated. Why would this lead us to suppose there is some contraphysical property distinct from B_NH instantiated in that world?

A natural explanation is available if, in reacting to the case, we implicitly make two assumptions. The first is that when a fact is fully grounded, there is no possible world in which the grounds obtain and the grounded does not.Footnote ¹³ The second is that physicalism is false if the fact that Amy has H lacks a full ground consisting solely of physical facts and, perhaps, facts to the effect that various entities do not exist or are not instantiated.

In considering the case, we first note that the physical facts in this world are not enough to ensure that Amy has H, since there is a physical duplicate of it (with the blocker added) in which she lacks H. Given the assumption that full grounds necessitate, we conclude that this fact about pain is not fully grounded by any physical facts. Given the assumption about physicalism, we conclude that if physicalism is true, the fact that Amy has H must have a full ground consisting not only of physical facts but also facts to the effect that such and such things do not exist or are not instantiated. But our understanding of pain makes it hard to believe that someone’s being in pain is grounded in any facts of the latter sort. (This, of course, is what the idea that pain is a “positive” property is getting at.) As a result, we are inclined to suppose that Amy’s having H does not meet the requirements on being physicalistically acceptable. Either there is some full ground of this fact that includes something other than the acceptable grounds or her having H has no full grounds distinct from itself and (hence) is fundamental.

In light of this account, we can offer a different, better definition of a TBR world. Instead of the previous version of condition (v) that spoke of “positive” facts, the new version refers instead to the grounding considerations just reviewed:

Recall that a nonphysical property was defined earlier as one that is not initially counted as physical but might be related to the physical in the way required for physicalism’s truth. Condition (v) here allows that the instance of F is fundamental, in which case it is not related to the physical in the way required for physicalism’s truth. Or, as per the second disjunct, it may be fully grounded in some fact involving a contraphysical property. Either way, condition (v) ensures the falsity of physicalism in w.

3.c The merely modal objection and the possibility of troublesome blockers

If this account of the distinction between innocent and troublesome blockers is accepted, the problem blockers pose for supervenience formulations of physicalism is a version of the more general merely modal objection. Perhaps the easiest way to see this is to note that condition (v)—the condition that ensures the falsity of physicalism—renders conditions (i)–(iii) idle. The structure of blocking is inessential to the troublesome character of the world.

Suppose we simplify the definition then by excising (i)–(iii) and removing mention of properties not playing a role in the remaining conditions. The simplified conditions define, let us say, a “troublesome” world:

A standard way to present the merely modal objection to supervenience formulations is to give a consistent description of modal space that both verifies the supervenience thesis in question and falsifies physicalism. Doing this will amount to describing a troublesome world as defined above.Footnote ¹⁴ If we succeed in conceiving of a troublesome blocker-relevant world, we will just be implementing the merely modal objection using an example of a particularly complicated type.

Can we conceive of such a world? In section 2, I examined at length an attempt to do so following the strategy suggested by Hawthorne, arguing that appeals to supernatural intervention gave us no good picture of a TBR world. The point was to show that our understanding of the blockers problem was inadequate and that we needed a better account of the distinction between innocent and troublesome blocker. Now we have that better account and, I believe, can conceive clearly of a TBR world.

To see how, let us think first about examples used to illustrate the merely modal objection. The simplest sort of example invokes fundamental necessities. Suppose that MPD is true, but there is no explanation of its truth; the fact that there is no minimal physical duplicate of the actual world that isn’t a duplicate simpliciter is just a brute fact. This is consistent with the claim that, say, Amy’s headache is an entirely new kind of property, one that is not grounded in or in any interesting metaphysical way linked to the physical properties she possesses at that time. In this case, physicalism is false; the first disjunct of condition (ii) applies here, as the nonphysical property is simply fundamental.

Insofar as we are doubtful about the possibility of such fundamental necessities, however, this way of making the merely modal objection has limited force. More effective examples are given when we are given some idea of how the relevant facts about modal space might be explicable. The best approach to my mind is one that exploits a kind of “common cause” structure, so that nonphysical properties of the relevant sort and the physical properties on which they supervene are both grounded in some third category of property, and this common grounding explains this supervenience. Here is one way to fill out the story a bit more (adapted from Witmer Reference Witmer, Gillett and Loewer2001, 70).Footnote ¹⁵

Suppose that there are properties of some contraphysical sort that are distinct from any of the nonphysical properties with which we are acquainted. Call them Q-properties. There are many different Q-properties; in fact, for every physical property P there exists a pair of Q-properties such that there are two ways P could be instantiated: it could be instantiated either by virtue of one member of that pair or by virtue of the other member. On this picture, Q-properties are more fundamental than physical properties. Fixing the Q-properties will fix the physical properties, of course, given the possible ways in which physical properties could be instantiated. Further, suppose that every other kind of property instantiated in the actual world—every nonphysical and nonQ property—is necessarily instantiated as well by virtue of the instantiation of Q-properties. The physical is entirely bypassed on this picture, so that even though, say, a headache supervenes on some physical property, this is just a side effect of the fact that both that physical property and that headache are grounded in some fact about these Q-properties.

Now what about troublesome blocker-relevant worlds? I will provide a version of the Amy example; to make it easier to digest, I will give it a playful gloss by imagining the contraphysical properties are both a kind of “spooky color.” Let spooky blue (B) be a contraphysical determinable property with two incompatible determinates B ₁ and B ₂ that exhaust the shades of B. One of these—B ₁—will serve as our blocker of H relative to N. The other will play a role in grounding the instantiation of H. Those roles depend on two further stipulations about the nature of N and H, both of which ensure that any instantiation of either N or H is grounded both in something contraphysical and something physical.

Let P be some physical property other than N; P might be fundamental in the way physicalists think all physical properties to be. The first stipulation is that it lies in the nature of N that to have N is to have both P and spooky blue B (the determinable spooky blue), so that, necessarily, anything with N has it by virtue of having both P and B. The second stipulation is that it lies in the nature of H that to have H is to have both P and the specific spooky shade B ₂, so that, necessarily, anything with H has it by virtue of having both P and B ₂. At a glance:

Given these claims about the nature of the relevant properties, we can describe a world that meets the condition on being a TBR world and presents no reasons to doubt its possibility. Let w_A be the world in question, where Amy has both N and H and nothing has the blocker property B ₁. Now let us review the conditions (i)–(v) on being a TBR world as applied to this example.

Condition (i) is that B ₁ blocks H relative to N. Given our stipulations, both of the following modal claims follow from the nature of the properties at issue. First, necessarily, if something has N, it has H as well, unless it also has B₁. If it doesn’t have B ₁ but has N, it must have B ₂ (since N is always grounded in either B ₁ or B ₂). And since having N always requires having P, this means that the individual in question has both P and B ₂—which grounds having H. Second, possibly, something has N and B₁ and doesn’t have H. When N is grounded by something having P and B ₁, that thing will not have B ₂ (as B ₁ excludes it) and hence does not have H (since H requires having P and B ₂).

Condition (ii) (that nothing in w_A has B ₁) and condition (iii) (that something in w_A has N) have both been stipulated to hold in the example.

Condition (iv) is that any minimal physical duplicate of w_A is a duplicate simpliciter of w. A minimal physical duplicate of w_A will replicate Amy’s possession of N, as N is a physical property. This requires inclusion of B, but this raises the question as to whether the duplicate shall have B ₁ or B ₂ in that place. Presumably, however, as the actual instance of N is grounded in B ₂, not B ₁, the minimal physical duplicate will also use B ₂, not B ₁. Substituting B ₁ would seem to be adding something not necessary for the physical duplication. So, in the minimal physical duplicate, Amy has N by having P and B ₂. As a result, she must also have H, as P and B ₂ necessarily ground H. So far as the factors discussed go, then, the minimal physical duplicate of w_A should be a duplicate simpliciter.

Finally, condition (v) is that for at least one thing x that has H in w_A , either the fact that x has H has no full grounds distinct from itself and is thereby fundamental or there is some contraphysical property C such that the fact that x has H is grounded (at least in part) in the fact that x has C. The contraphysical property B ₂ may stand as the required C. One thing in w_A with H is Amy, and in her case the instantiation of H is grounded at least partly in her having that contraphysical B ₂. B ₂ renders true the existential claim that there is some contraphysical property that helps ground the fact that Amy has H. The second disjunct of (v) is thus satisfied.

We have, then, an example of a TBR world where nothing about it suggests we should distrust its appearance of possibility. So in this way the blockers problem is vindicated; it can be used to show that a supervenience thesis like MPD is too weak for physicalism. But this vindication is not much to celebrate. It is—as we just saw in this example—a much more complex way to make a point that can be made without invoking blockers.