Haecceitism and Symmetry-Breaking: Things, Time, and Powers

3.1. The Line of Resistance

The first turns on understanding the second-rate status of non-qualitative matters in terms other than ground. Consider (think ‘only qualitative matters are determinate’):

(Qual-D) All non-qualitative facts are indeterminate.

Russell (2015; 2016; 2018) articulates the distinction between “determinate” (or “factual”) and “indeterminate” (“non-factual”) matters, and his 2015 (409) and 2018 (564–565) understand qualitativism in terms similar to Qual-D. And he seems to think CCPs give qualitativists a reason to prefer Qual-D over -G. At any rate, in (2015) he offers them a Qual-D-based line of resistance, and in (2016) he frames Bet and Gimel as posing a special challenge for Qual-G (as does Sider in [2020: 203]).

Following Russell, determinate or factual matters correspond to how the world is in itself, to its objective structure. Indeterminate or non-factual matters, by contrast, fall short. Even if aptly uttered and true in some “thin” sense, non-factual claims ascribe structure to the world that isn’t really there. Being indeterminate doesn’t seem to imply being grounded (cf. Sider 2011: 126; Dasgupta 2020: 141–143). Suppose, for example, that a person, P, undergoes a physically or psychologically disruptive procedure (cf. Russell 2015: 400, fn 13), that we think it’s indeterminate whether P survives, and that we arbitrarily grant the (non-factual) truth of ‘P survives.’ Because of this (thin) truth’s arbitrariness, we may deny that it’s grounded in further truths. Nor does being grounded seem to imply being indeterminate. For example, conjunctions and disjunctions of determinate facts are determinate, but presumably grounded (Russell 2015: §6; 2018: 566). So, Qual-G and -D provide different accounts of metaphysical second-rate-ness. It’s one thing to ground the non-qualitative, another to erase its objective reality.

(In §1 I glossed “fundamental” facts as facts not grounded in further facts, and assumed that every non-fundamental fact is grounded in fundamental ones. But having distinguished determinate and indeterminate matters: By “fundamental” facts I mean determinate facts not grounded in further facts, and I assume that every determinate non-fundamental fact is grounded in fundamental facts.)

How does Qual-D lend itself to a response to CCPs? As Russell (2015) explains, Qual-D-ers may say that the differences between the relevant worlds are non-factual. When we put on our factualist glasses (that filter out indeterminate facts) (403), the differences vanish. If we apply this line of thought to Bet and Gimel, they turn out to be the same possibility, differently conceived. In the same vein, we can note that Qual-D doesn’t imply §1’s anti-haecceitism, if the latter implies that any fact whatever—determinate or indeterminate—must be fixed by qualitative facts. The key modal claim is that qualitative matters fix how the world is in determinate respects.

My problem with Qual-D and the accompanying “no-factual-difference” response to our CCP is that they simply aren’t credible unless we reject Things. (Having distinguished determinate and indeterminate matters, I understand Things as saying that it’s possible, not simply that material things exist, but that they determinately exist, and similarly with the other clauses.) I defend the judgment that Qual-D is credible only if Things is false in §3.2. It won’t follow that the no-factual-difference response is credible only if Things is false, since Qual-D is just one possible basis for denying that Bet and Gimel factually differ. But I think that other ways of denying that they do also require tampering with Things; I give two examples in §3.3.

3.2. Qual-D and Things

Suppose that Alef were actual, that we’re speaking from that world, as it were. Given §2’s description of this world, it’s natural to take these facts to determinately hold:

(N) Cas and Pol are material spheres a foot apart for one second.

(Q) ∃x∃y(x and y are material spheres a foot apart for one second).

Non-qualitative fact N is an instance, or witnessing fact, for Q, a qualitative existentially quantified fact. ‘Cas’ and ‘Pol’ are simply our names for the particular spheres that determinately exist, if any do; hence ‘N’ simply picks out the particular instance of Q that determinately holds, if any does.

Now according to Qual-D, determinate non-qualitative facts are impossible. So assuming the world before us is possible, we must re-describe it. (And I assume there is a possibility in the vicinity to be described. If Qual-D can’t accommodate this, it’s a non-starter.) At a minimum, we must strike N from determinate reality: There are no particular spheres such that they determinately exist. But what about Q? Can we keep it, or must we strike it from determinate reality as well?

I think striking N would require us to strike Q too. Let ‘Det’ be a determinacy sentence operator (‘determinately’), and consider this conditional:

(C₁) If Det, ∃x∃y(x and y are material spheres a foot apart for one second), then ∃x∃y(Det, x and y are material spheres a foot apart for one second).

This says, in effect, that if Q determinately holds, there’s a Q-instance such that it determinately holds too. I find C₁ compelling. If it’s determinately the case that there’s a material sphere over there for a stretch of time, then surely there’s a particular sphere such that the sphere over there is determinately it. Despite its seeming obvious, I’ll say a bit more in C₁’s defense.

Let’s introduce a fictional observer, O, into the world before us. Now suppose that C₁’s antecedent holds, that O is attending to (e.g., looking at, or touching) a sphere, and consider:

(C₂) If Det, ∃x(x is a material sphere that exists for one second & O perceives x), then ∃x(x is a material sphere & Det, O perceives x).

Intuitively: If it’s determinately the case that O perceives an enduring material sphere, then there’s a particular one O determinately perceives. I find C₂ compelling. If O determinately perceives such a sphere, he could name it and express apparently determinate facts about it. He might call it ‘Ursula’ and say ‘Ursula is spherical,’ thereby apparently expressing a determinate non-qualitative fact.

Now I can think of circumstances in which, despite appearances, no particular sphere is determinately perceived, but they are circumstances in which C₂’s antecedent fails. Perhaps the world before us doesn’t really have any “sphere structure.” Perhaps all we (determinately) have are particles arranged sphere-wise, or universals stitched together sphere-wise, or a cosmos with a “sphere-over-there” property, or a mind with a “sphere-over-there” experience. In any such case, I can understand how there’s no particular sphere that’s determinately perceived. But that’s because there isn’t, determinately, any sphere there at all, contra C₂’s antecedent.

Alternatively, suppose we really have sphere structure before us, but that it’s in flux. Suppose that O attends to what appears to be a single sphere for one second, but that halfway through this interval a demon annihilates the initial sphere and seamlessly replaces it with another. This doesn’t yet cast doubt on C₂’s consequent; indeed there now seem to be two spheres each of which is such that O determinately perceives it. But if we ramp up the demonic activity by adding more acts of replacement, you might start to doubt that any particular sphere is determinately perceived. But these demon cases falsify C₂’s antecedent, which concerns a sphere that exists for a whole second.

C₂ will take us to C₁ if we add a premise to this effect: Whether determinate existentially quantified facts about material spheres have determinate instances doesn’t depend on whether the spheres quantified over are observed. This also seems compelling. If the world before us determinately contains material spheres, then the fiction about O teaches us something about what this world is like sans O. There are determinate non-qualitative facts there to be discovered.

Here’s my best attempt to cast doubt on C₁. Consider a world, Rep, in which an initial sphere, a, is replaced with another, b, and suppose that, for some instant, t, it’s metaphysically unsettled¹⁴ whether the sphere at t is a or b. This seems to falsify C₃:

(C₃) If Det, ∃x(x is a material sphere at t), then ∃x(Det, x is a material sphere at t).

The idea is that the antecedent holds, but not the consequent, since neither Det, a is a material sphere at t, nor Det, b is a material sphere at t. Granting C₃’s falsity, you might think this casts doubt on C₁ (and C₂). If a sphere can lack a determinate thisness at an instant, why not over an interval?

However, I see no reason to think that the state of affairs at t in Rep could obtain over Alef’s entire history. We’ve seen no reason to doubt that Rep has two spheres, each with a determinate thisness. It’s just that, at t, it’s indeterminate which thisness (a’s or b’s) is instantiated. So: The then-existing sphere’s thisness is “poised between”¹⁵ (a.) determinately instantiated alternatives; we have a basis for determining (b.) how many (two) and (c.) which ones (a’s and b’s); and we (d.) can explain why the thisness is so poised (in terms of details about the sphere-replacement process). Now if we try to transpose the t-Rep state of affairs to Alef, the idea is that each sphere’s thisness is, for the entire second, poised between alternatives. But in this transmogrification, (a.)–(d.) all seem to fail.

Further, suppose we grant that the t-Rep state of affairs obtains in Alef, and so reject C₁. Since the thisness of Rep’s t-sphere is poised between a’s and b’s, we still get a determinate, albeit disjunctive, non-qualitative fact about this sphere: Det, a is a material sphere at t or b is a material sphere at t. So turning to the Alef transposition, there will still be determinate, albeit disjunctive, non-qualitative facts. And Qual-D-ers can’t accept this.¹⁶ They think reality lacks non-qualitative structure, not that it has such structure but that it’s indeterminate which bits of it obtain. (It’s the former idea that facilitates the no-factual-difference line of resistance. In §4 we’ll consider a different line, which seems to trade on the latter idea.) So on the present attempt to cast doubt on C₁, it would turn out false (if at all) for a reason Qual-D-ers can’t accept. So they aren’t in a position to object to C₁, or to affirm Q’s determinacy while denying N’s, on this basis.

Now if the world before us, i.e., Alef, indeed contains a determinate Q-instance (N), it needn’t be fundamental; determinate facts may be grounded (§3.1). According to what Dasgupta (2017) calls ‘quantifier generalism,’ we may say that Q is fundamental and grounds N.¹⁷ According to Dasgupta’s (2009; 2017) “algebraic generalism,” the fundamental facts exclusively concern universals. So algebraic generalists may say that Q and N are both grounded. There are other, more exotic proposals as well for what the fundamental facts are like.¹⁸ My point here is just that C₁’s consequent is perfectly consistent with qualitativism, because consistent with Qual-G. Indeed, C₁ itself is perfectly consistent with Qual-D, since Qual-D-ers may deny the antecedent. This is precisely what I’ve argued: not that Qual-D is false per se, but that Qual-D-ers must strike Q from determinate reality.

Let’s return to Things. Clause T₁ says that it’s possible that material things determinately exist. If this is true, we may stipulate that Alef really has “material-thing structure,” and Qual-D looks doomed. For a determinate fact will presumably capture thing structure by either “naming” particular things (cf. N) or quantifying over things, as Q does. Qual-D-ers can’t accept determinate non-qualitative facts, and I’ve argued that they can’t accept Q’s determinacy either. And while would-be T₁-affirming Qual-D-ers might propose an alternative quantified fact (for example, by eschewing composite spheres in favor of simples), it seems that any alternative that could plausibly capture Alef’s thing structure will be susceptible to the same sort of argument I’ve made about Q. I conclude that Qual-D is credible only if T₁ is false. Qual-D-ers may accept algebraic generalism about determinate reality (sans any grounded facts of Q’s or N’s forms), or some other things-purging proposal. I also note that Russell (2018) argues that Qual-D-ers should deny that quantification over things is “metaphysically perspicuous” (cf. 2015: 414). Though this isn’t the same as maintaining that they should deny that facts like Q are determinate, it seems quite close.

3.3. Other Things-Rejecting Lines of Resistance

Here are three Things-rejecting lines of resistance to our CCP that don’t depend on Qual-D.

First: Reject T₁ by affirming the necessity of idealism, and take Alef to consist in a mind’s having a visual experience of two spheres for one second. Now Bet and Gimel are no longer nm-duplicates. For only in one will it be true that a mind sees a sphere on the left of its visual field for two seconds and a sphere on the right for one. However, we can get two nm-duplicates by adding a mind. Consider a world in which one mind sees a left-side sphere outlive a right-side one and another sees a right-side sphere outlive a left-side one, and a world in which the experiences are distributed the other way round. And I think that the prospects for resisting this CCP depend on the same sorts of considerations that I discuss in §§4–7 in connection with our CCP.

Second: Affirm PII and the possibility of bi-location, and take Alef to contain a single bi-locating sphere. This precludes T₃. Now Bet and Gimel are no longer distinct: In both there’s a sphere that bi-locates for one second and “uni-locates” for an additional second. However, this line of resistance’s prospects are abysmal. The possibility of multi-location (by things, across space) is controversial enough as it is,¹⁹ and this line says that qualitatively identical things are necessarily single, multi-locating things. Further, we still get two nm-duplicates if substantival space is possible. For then we take Bet and Gimel to differ over which region enjoys two (one) second(s) of occupation.

Third: Affirm the necessity of existence monism,²⁰ and that fundamental properties must be qualitative. (This precludes T₁ if we insist on the plural ‘things’ therein.) Now Bet and Gimel are no longer distinct (Sider 2007: 4–5). However, committing to existence monism’s necessity would be quite a steep price to pay to resist our CCP.

3.4. Taking Stock

I said (§3.0) that recent work on qualitativism has proposed two lines of resistance for our CCP. The first embraces Qual-D and denies that Bet and Gimel factually differ (§3.1), and I’ve argued that this is credible only if you reject Things (§3.2). I’ve also noted two other ways of denying Bet’s and Gimel’s distinctness that reject or at least qualify Things (§3.3). I haven’t argued for Things, and so if you find it implausible, perhaps one of these lines of resistance is for you. But it’s certainly worth looking for Things-consistent lines, as vast swaths of the metaphysical landscape rest on this framework. I emphasize that rejecting T₁ doesn’t just require striking material things from your fundamental ontology; they can’t determinately exist at all.

From now on, we grant Things. Accordingly, from now on we understand qualitativism via Qual-G. So qualitativists accept determinate non-qualitative facts; they just insist that they’re grounded in and so (by G-Fix) fixed by qualitative ones. And from now on we take Alef to determinately contain two particular material spheres, assume that it’s possible, and take Bet and Gimel to be distinct nm-duplicates (differing over which of those spheres outlives the other).

4.1. Russell’s Offer to Qual-G-ers

Russell (2016) discusses Bet and Gimel, specifically as a threat to Qual-G. Or rather, he discusses Adams’s version of the CCP (1979: 22). Adams raises three worlds, w₁–w₃, corresponding to Alef, Bet, and Gimel. But w₁’s spheres “have always existed and always will exist,” hence the CCP-worlds each disrupt w₁’s symmetry by shortening a (different) sphere’s life. Our CCP-worlds, by contrast, disrupt Alef’s symmetry by lengthening (a different) one. Having acknowledged that Russell doesn’t discuss our world trio, I’ll adapt his discussion of Adams’s to ours.

Suppose Alef were actual, let Q be a proposition capturing Bet’s and Gimel’s nm-qualitative character, and assume Q is possible. So in fact there are two spheres, Cas and Pol, that exist for one second. But it could have been the case that Q held, in which case there would have been two spheres, one of which exists for an additional second.

Russell seems to think Qual-G-ers must also say that, were Q to have held, the spheres would necessarily (hereafter just ‘would’) have been Cas and Pol, such that one of them would have existed for an extra second (2016: 316, 330). Let’s call this ‘Disjunction’:

(Disjunction) Q would have fixed that either Bet or Gimel is actual.

If this is right, it also seems that Qual-G-ers must affirm:

(Disjunct) Either Bet or Gimel is such that Q would have fixed that it is actual.

For if Q would have left open which sphere gets the extra second, some non-qualitative facts wouldn’t have been qualitatively grounded. But Russell finds Disjunct problematic. The idea that one of these spheres is such that it must be the one whose life would be lengthened amounts to an “odd” and “surprising” “de re determinism” (316). He then proposes that Qual-G-ers can “put a better [and brave] face” on Disjunct by adding some indeterminacy (in §3.1’s sense): While Bet or Gimel is such that Q would have fixed its actuality, it’s indeterminate which (316–319, 330).

So on this proposed line of resistance, from Alef’s perspective exactly one of Bet and Gimel is possible, with the added twist that it’s indeterminate which. Now though Russell thinks this indeterminacy makes the proposal’s core more palatable, it leads to a problem: Indeterminacy in modal matters is “infectious,” liable to spread to non-modal ones (2016: 319–327). Let Dup (think ‘duplicate of Bet and Gimel’) be the world that would be actual were Q to hold. If it’s indeterminate in Alef which of [Cas outlives Pol] or [Pol outlives Cas] Q would fix, then if we hop over to Dup and speak as if it were actual, it seems that reality is poised between Bet and Gimel:

(Indet) It’s indeterminate whether Cas outlives Pol or Pol outlives Cas.

And Qual-G-ers shouldn’t like this.²¹ To stop the spread, Russell advises taking the modal indeterminacy to be contingent (327–328): Though it’s indeterminate in Alef whether Q would fix [Cas outlives Pol] or [Pol outlives Cas], if we hop over to Dup one of them is such that Q determinately fixes it (contra Indet). In the end, he takes this proposal, along with the advised method for containing the indeterminacy, to be Qual-G’s “best hope” (330).

I think Qual-G-ers can do better; I present one alternative line of resistance in §4.3, and another in §5. On the latter, we say that Q would have grounded the existence of different spheres, such that Bet and Gimel are both impossible and Disjunction and Disjunct both false.²² In the rest of this section, I argue that Russell’s offered line and the §4.3-line face serious problems.

4.2. Exactly One is Possible?

Instead of tempering Disjunct with some modal indeterminacy and then containing the latter (as Russell advises), we might take Disjunct straight (no indeterminacy), or let the indeterminacy spread (more indeterminacy). But all three lines of thought accept Disjunct, which Russell admits is odd and is what leads to the view that exactly one of Bet and Gimel is possible. I’ll now argue that Disjunct-based lines of resistance face serious problems.

Since Cas and Pol are in fact (i.e., in Alef, which we’re taking to be actual) exactly alike in nm-qualitative respects, it follows by Feature-SV (§2) that they’re exactly alike in all qualitative respects. But consider these qualitative modal relations:

x bears R₁ to y iff necessarily, if Q holds then x outlives y.

x bears R₂ to y iff possibly, Q holds and x outlives y.

If Q would have fixed Bet’s actuality, then Cas bears R₁ and R₂ to Pol while Pol bears neither to Cas. And if Q would have fixed Gimel’s actuality, Pol unrequitedly bears them to Cas. So, Disjunct-ers reject Feature-SV: Cas and Pol break symmetry in modal qualitative respects despite their perfect symmetry in nm-qualitative respects. But Feature-SV seems very plausible. Even philosophers who affirm distinct material coincidents (e.g., statues and constituting masses) will typically identify nm-qualitative differences (e.g., differences in kind) to accompany the modal ones.

Further, Disjunct-ers can’t accept perhaps the most principled position on which Feature-SV would be false. You might reject Feature-SV because you think as a general matter that nm-qualitative matters fail to fix modal qualitative ones. So for example, you think there are multiple possible nm-duplicates of Alef that differ over the distribution of modal qualitative features. In one, neither sphere bears R₂ to the other; in a second, just one bears R₂; in a third, both bear R₂. But Disjunct-ers can’t accept a possible nm-duplicate of Alef whose spheres both bear R₂. For were there such a world, we could stipulate that ‘Alef’ refers to it and that “Bet” and “Gimel” concern its spheres, falsifying Disjunct. So Disjunct-ers affirm that Alef’s nm-qualitative character fixes its complete qualitative character; they just say that the fixed distribution of modal features is one on which exactly one sphere bears R₂ to the other.

Further problems loom when we ask Disjunct-ers to say more about Cas’s and Pol’s modal profiles. Letting Bet be the possible member of our CCP (so Cas unrequitedly bears R₂ to Pol), Alef’s and Bet’s possibility and Gimel’s impossibility imply that Cas can exist for one second if Pol does too, that Cas can exist for two seconds if Pol exists for one, and that Pol can’t exist for two seconds if Cas exists for one. But this leaves a lot open. Does our Disjunct-er think Cas can only exist for either exactly one or exactly two seconds? Does he think Cas’s ability to exist for any duration depends on Pol’s existing for exactly one? Here’s one natural way of filling out the view: (a.) Cas and Pol can exist together for any amount of time (not just one second, as in Alef), (b.) Cas can outlive Pol by any amount (not just one second, as in Bet), but (c.) Pol can’t outlive Cas (to avoid GCPs).

However, this way of filling out profiles commits Disjunct-ers to mysterious non-local dependencies. At any time at which Cas and Pol exist, each is capable of dying and of persisting (by (a.)). However, Cas can’t actualize the first capacity unless Pol does too ((c.)). If Pol doesn’t, Cas must actualize the second capacity. And Pol can’t persist unless Cas does too ((c.)). If Cas dies, Pol must too. Such dependencies are mysterious.²³ How could Pol’s persisting, over here, force Cas, over there, to actualize its capacity to persist and prevent Cas from actualizing its capacity to die? How could Cas’s dying force Pol to die and prevent Pol from persisting?

Suppose, on the other hand, that our Disjunct-er denies this way of filling out profiles. Suppose he says that Pol must exist (if at all) for exactly one second (contra (a.)). So at the one-second-mark, Pol no longer has the capacity to persist, and so Cas can’t do anything that would non-locally thwart Pol from actualizing such a capacity. But if he says this to avoid non-local dependencies, it looks ad hoc. And in any case, it seems arbitrary and unprincipled. Why should Pol be capable of existing for only exactly one second, given that Cas can exist for multiple intervals? To be sure, by virtue of accepting Disjunct our Disjunct-er is committed to some sort of asymmetry between Cas’s and Pol’s modal profiles. But we’re presently considering how to fill out this asymmetry, and the worry is that ways of doing so that avoid non-local dependencies will be arbitrary and unprincipled.

Thus far we’ve considered only modal asymmetries concerning duration. But applying the present line of resistance to other CCPs will lead to more asymmetries. Consider a world like Alef except in that Cas turns blue (or is replaced with a blue sphere) after half a second, or in which a cube appears above Cas (i.e., next to it in a direction orthogonal to the one in which Pol lies) after half a second. Each world is one member of a CCP, the other being a world in which Pol turns blue, or acquires a hovering cube. And to apply the line to these CCPs, we posit more modal relations borne by just one sphere. To illustrate, let W₁ be a world in which Cas turns blue and Pol yellow, W₂ be an nm-duplicate in which it’s the other way round, and consider:

x bears R₃ to y iff possibly, after half a second x turns blue and y yellow.

To resist this CCP in the same way as the Bet-Gimel one, our Disjunct-er will say that just one of Cas and Pol bears R₃ to the other in Alef, such that just one of W₁ and W₂ is possible.

Now, our Disjunct-er doesn’t have to resist the W₁-W₂ CCP in the same way as the Bet-Gimel one. He might say that W₁ and W₂ are both possible, but not duplicates. For if Cas and Pol break symmetry over R₂, we get a qualitative difference between W₁ and W₂. In only one world will it be true that a sphere that could have outlived the other turns blue. The general point here is that, as long as Cas and Pol break symmetry over one qualitative modal relation, we get qualitative differences between any two nm-duplicates that differ over which nm-qualitative roles Cas and Pol get. If our Disjunct-er resists the W₁-W₂ CCP in this way, then he rejects not just Feature-SV but Fact-SV (§2) too.

However, if our Disjunct-er wants to deal with various CCPs concerning Cas and Pol by positing just one symmetry-breaking modal relation, why should it be R₂, instead of R₃ or some other one? If R₂ is the symmetry-breaker, one of Bet and Gimel is possible and W₁ and W₂ are both possible. If R₃ is, one of W₁ and W₂ is possible and Bet and Gimel are both possible. It’s hard to see how there could be a principled basis for singling out one of these relations to be the privileged symmetry-breaker. To avoid this problem, our Disjunct-er can say that Cas and Pol break symmetry over all of them. So just one of Bet and Gimel is possible, as is just one of W₁ and W₂, and so on. But this is also problematic. Even if you’re open to Feature-SV’s falsity, you might find it implausible that Cas and Pol differ in so many modal respects. Further, adding asymmetries raises uncomfortable questions about how to pair them. Supposing that just one of Cas and Pol bears R₂ to the other, and likewise with R₃, are R₂ and R₃ borne by the same sphere, or by opposite spheres? We can’t say that one sphere is always “the bearer,” since both spheres are always bearers. For instance, if just Cas bears R₃ to Pol, then just Pol bears a converse relation to Cas.

Let’s review. Resisting the Bet-Gimel CCP by affirming Disjunct requires rejecting Feature-SV (a plausible principle), and without being able to integrate that rejection within a more general position on which nm-qualitative matters fail to fix modal ones. Further, when we try to fill out what Disjunct-ers should say about Cas’s and Pol’s modal profiles, further problems arise. On some ways of doing so, we get mysterious non-local dependencies; on others, seemingly arbitrary and unprincipled gaps in Cas’s or Pol’s capacities. Moreover, when we try to fill out profiles so as to deal with other CCPs, we face a choice between a problematic explosion of symmetry-breaking modal relations and an unprincipled selection of just a few (e.g., R₂ and its converse, or R₃ and its converse, etc.).

Would adding the indeterminacy discussed in §4.1 alleviate any of these problems? It lets Disjunct-ers say that though Cas and Pol break symmetry in some modal qualitative respects, it’s indeterminate which sphere is the bearer of any given symmetry-breaking relation. Relatedly, it lets them say that, though Feature-SV is false, this principle isn’t:

(D-Feature-SV) Determinate qualitative features are fixed by determinate nm-qualitative features.

However, it’s not clear whether the above problems’ force depends on there being determinate facts about which thing bears any given relation. Even if D-Feature-SV is salvaged, it’s still determinately the case that Cas and Pol break symmetry in modal qualitative respects. Further, even if adding the indeterminacy helps with some of the above problems, it doesn’t follow that it delivers a better line of resistance. For adding it may raise problems of its own. I think it would, though won’t elaborate. I think it’s clear that Disjunct-based lines face serious problems.

4.3. Not Duplicates?

According to the line of resistance I’ll now sketch, we say that Bet and Gimel, though possible nm-duplicates, aren’t duplicates (thereby rejecting Fact-SV). We’ve just seen how this would work: Qual-G-ers may say that Cas and Pol bear R₂ to each other, such that Bet and Gimel are both possible, as long as they also say that Cas and Pol differ over some other qualitative modal relation (e.g., R₃), such that Bet and Gimel aren’t total duplicates. The problem was that there seemed to be no principled basis for taking Cas and Pol to bear R₂ to each other while breaking symmetry over other relations.

However, thus far we’ve only considered diachronic modal relations: ones concerning what can happen over time (e.g., R₂, R₃). Perhaps we can identify a principled symmetry-breaker by turning to synchronic modal relations. If Cas and Pol differ over a qualitative relation concerning their origins, Qual-G-ers can resist all CCPs whose worlds begin the same as Alef (Bet and Gimel, W₁ and W₂, etc.) in the same way (denying that the worlds are duplicates).

Here’s one proposal: Only one of Cas and Pol could have originated by itself. Imagine God’s creating the first time in Alef by unrolling a map from left to right. (So the whole map concerns a single time.) If he unrolls it just a bit, only Cas (say) appears; if he unrolls it further, Pol does too. So letting R₄ be a qualitative modal relation that one thing bears to another iff, possibly, the former comes to exist without the latter, suppose that Cas (say) unrequitedly bears R₄ to Pol. And suppose that Cas and Pol bear R₂ to each other. Now Bet and Gimel are both possible, but not duplicates. Only in Bet does a sphere that could have originated by itself outlive another sphere.

This line of resistance seems more plausible than the preceding one, which turned on at least some diachronic modal asymmetries between Cas and Pol in Alef. I find it more credible that Cas and Pol differ over R₄ than that they differ over R₂ or R₃. Further, differing over R₄ wouldn’t seem to give rise to mysterious non-local dependencies. Moreover, as just explained this line seems to have a principled basis for resisting a vast array of CCPs by appealing to just one symmetry-breaker in Alef.

Still, this line of resistance seems implausible. Like the prior line, this one rejects Feature-SV, and without being able to integrate that stance within a more general position on which nm-qualitative matters fail to fix modal ones. (Just as with the prior line, on this one Alef’s nm-qualitative character fixes the distribution of modal features.) And even if this line’s symmetry-breaking modal relation isn’t as objectionable, there nevertheless seems to be no (non-ad-hoc) reason to think that our spheres would break symmetry in this way.

Further, even if the present line can handle CCPs whose worlds begin the same as Alef, problems arise when we seek to apply the line to others. Consider a world, W, in which four spheres exist in a line for one second, and a W-based CCP whose worlds differ over which half of the line gets an extra second. How would R₄ be instantiated in W? Should we start on one end of the line, and say that that sphere bears R₄ to the next, which bears it to the next, and so on down the line? Should we take one of the middle spheres to be the prime R₄-bearer? It’s hard to see how there could be any principled stance about this.

5.1. Theories about Time

Suppose there was war yesterday but peace today. How should we understand the temporal variation? We might think the facts themselves change. It was the case that there’s war, but is now the case that there’s peace. Or we might locate the variation in the content of the facts. For example, there’s a fact to the effect that a particular war-like worldly state is earlier than a peace-like one. On the “dynamic” or “A-theory” of time, the facts may change,²⁵ which I’ll understand in terms of accepting tense operators (e.g., ‘it was the case that’) in one’s fundamental ideology.²⁶ On the “static” or “B-theory,” all temporal variation is ultimately understood via content-variation.²⁷

Some A-theories differ over temporal ontology. On presentism, (always) only present goings-on exist; on the growing-block view, (always) only past and present ones do; and on the (moving-)spotlight view, (always) past, present, and future ones do. So some A-theories invoke change- and content-variation. If we have a temporally extended block, we get content-variation; and if the block changes (e.g., by growing, or a part’s becoming present), change-variation.

I said (§2) that by ‘world’ I mean a maximally specific way for reality to be across all time. On the B-theory, such may be represented via a set of propositions; for instance:

{t₁ is earlier than t₂, there is war at t₁, there is peace at t₂}.

Since A-theorists think the facts may change, they may represent a world via a sequence of sets; for instance:

<{there is war}, {there is peace, it was the case that there is war}>.

B-theoretic worlds are duplicates if the relevant sets have the same qualitative facts, A-theoretic ones are if they have the same sequences of such facts, and B- and A-theoretic worlds are never duplicates. In fact it’s probably misleading to use the same word for what B- and A-theorists represent. Though I’ll still use ‘world’ in this way, I’ll also say that an A-theorist’s sequence represents a “(world) progression.” So the above sequence (an abstract item) represents a progression (a worldly matter). And I’ll call the worldly correlates of individual sets ‘times.’²⁸

Since earlier formulations of key theses (Qual-G, G-Fix, etc.) lack tense operators, those formulations fit well with the B-theory. If there was war yesterday but peace today, the B-theorist will say that there are, tenselessly, some fundamental facts that ground, tenselessly—and so fix—yesterday’s and today’s goings-on. And if he’s a Qual-G-er, he’ll say the fundamental facts are all qualitative. The A-theorist will presumably say that there were fundamental facts that grounded (then) the war, but that there are (now) fundamental facts that ground (now) peace. And if he’s a Qual-G-er, he’ll presumably say the fundamental facts are always all qualitative. So A-theorists should presumably add ‘always’ operators to our formulations. For instance:

(Fact-SV) Always, qualitative facts are fixed by nm-qualitative facts.

(Qual-G) Always, all non-qualitative facts are grounded in qualitative ones.

(G-Fix) Always, if some facts ground another, then the former modally fix the latter.

(Anti-haecceitism) Always, all facts are fixed by qualitative ones.

If we consider a toy progression with just two times (represented by a sequence with just two sets), then the above theses, so formulated, imply that the first time’s nm-qualitative facts fix all qualitative facts therein, which ground and so fix all other facts therein; and likewise with the second time.

We might call anti-haecceitism so transposed time anti-haecceitism, since it implies that, for every time within a possible world progression, that time’s facts are fixed by its qualitative facts. Progression anti-haecceitism, by contrast, just says that, for every possible world progression, the progression of facts is fixed by the progression of qualitative facts. Time anti-haecceitism certainly implies progression (and similarly with other theses, for instance time vs. progression Qual-G); whether the converse holds isn’t as clear. On the one hand, we can imagine scenarios that threaten time theses alone.²⁹ On the other, it isn’t clear that bare progression theses (progression theses plus the negation of time ones) are ultimately intelligible. Progression Qual-G, for instance, is the view that any possible progression of non-qualitative facts would be grounded in a qualitative progression. But progressions aren’t real things (it’s always the case that only part of one is real), and reality seems necessary for entering into grounding relations.

When key theses come up in A-theoretic contexts in what follows, I have time (‘always’) versions in mind unless otherwise noted.

5.2. The B-theory and New-Spheres

B-theorists take facts about the sweep of history to hold tenselessly. Accordingly, they can say that, were Alef’s nm-qualitative character to hold, Cas’s and Pol’s existence would be grounded, but that, were Dup’s to hold, the existence of different spheres would be. They also might not say this; I’m not claiming that they must run new-spheres (or resist our CCP at all), just that they can.

Now this line requires saying that the qualitative grounds in Alef for Cas’s and Pol’s existence don’t hold in Dup. For if they did, then by G-Fix Cas and Pol would exist there too. But Qual-G-ers are well-positioned to say this for reasons that are independent of any desire to resist CCPs.

Dasgupta (2017: 15–16; cf. 2009: 55–56) argues that Qual-G-ers should accept a sort of holism, to the effect that the fundamental qualitative grounds for the existence and features of interrelated things are encapsulated in a single fact. I’ll illustrate with quantifier generalism (§3.2). Let S₁ be a situation in which an F thing Rs a distinct G thing, and S₂ one in which the relation is different (R*-ness). On non-qualitativism, S₂’s fundamental facts might overlap S₁’s:

Fa         Gb         Rab                                  Fa           Gb          R*ab

But on qualitativism, such facts aren’t fundamental. And quantifier generalists shouldn’t simply substitute Ramsified variants. Note that [∃x(Fx)], [∃x(Gx)], and [∃x∃y(Rxy)] are consistent with, for example, there being one F and G thing that Rs itself. So instead of positing multiple facts each containing one predication, we posit one fact containing multiple predications:

∃x∃y(Fx & Gy & Rxy & ~(x=y))                        ∃x∃y(Fx & Gy & R*xy & ~(x=y))

As a result, S₂’s fundamental facts won’t overlap S₁’s; we exchange S₁’s for a new one.

As applied to Alef and Dup: We can say that, in Alef, there’s a single fundamental fact to the effect that two spheres exist for one second, and that, in Dup, there’s instead one to the effect that two spheres exist for one and two seconds respectively. In which case, the grounds for [Cas and Pol exist] in Alef won’t hold in Dup. Perhaps this sort of holism isn’t necessary for denying that the grounds hold in Dup; but it seems sufficient, and independently motivated for Qual-G-ers.

So, the B-theorist can deny that possibility is preserved through the “expansion operations” on Alef whereby Bet and Gimel were introduced (§2). To suppose that one sphere outlives another is to change the world’s fundamental tenseless character, which (he can say) changes which things exist. Let’s also now revisit §2’s Time argument for our CCP’s genuineness:

(Time) The histories of Alef, Bet, and Gimel are identical for the first half of a second, differing only as to how that shared initial segment is extended. And since the segment could, supposing Alef is possible, be extended in a way resulting in Alef’s actuality, surely it could be extended so as to actualize Bet instead, and likewise with Gimel.

And call the premise in the first line ‘SS’ (‘shared segment’). On the B-theory, we take SS to mean that the fundamental facts that constitute the first half-second of the “Alef-block” are the same as those constituting the first half-second of the Bet- and Gimel-blocks. So understood, the inference to Bet’s and Gimel’s possibility is natural. For it follows from SS and Alef’s possibility that there’s a possible collection of fundamental facts F₁, F₂, etc. such that (a.) F₁, etc. constitute the first half-second of Alef’s, Bet’s, and Gimel’s histories, and (b.) F₁, etc., are compossible with an additional collection G₁, etc. that together with F₁, etc. constitute the entirety of Alef’s history. And why should F₁, etc., be compossible only with G₁, etc., and not also with a different collection that together with F₁, etc. would constitute Bet’s history, and similarly with Gimel? However, on this reading of SS, B-theorists can deny it. They can say that the fundamental facts constituting the first half-second of Alef span Alef’s entirety (and include totality information about the spheres’ duration), and so at least partly differ from the fundamental facts that would constitute the first half-second of any possible nm-duplicate of Bet and Gimel. On the qualitativist holism sketched above, there may be no overlap at all. And while there may be other, metaphysically shallow readings of SS on which B-theorists must affirm it (e.g., the worlds “look the same” for the first half-second), such readings won’t sustain an inference to Bet’s and Gimel’s possibility.

5.3. A-theories and New-Spheres

I’ve explained how B-theorists can resist our CCP by saying that Dup’s spheres aren’t Cas and Pol. I now explain how some A-theorists can too, and argue that others can’t.

On A-theories, the facts don’t hold tenselessly, but rather unfold over time. So we think of Alef and Dup as world progressions (§5.1). Now consider (1) and (2):

(1) Alef and Dup begin with the same nm-qualitative facts. (That is, the Alef-progression’s first time and the Dup-progression’s first time have the same nm-qualitative facts.)

(2) Alef begins with [Cas and Pol exist].

They seem plausible. Alef and Dup prima facie appear to begin the same, qualitatively, and (2) seems to follow from Alef’s description (§2) on an endurantist view of persistence.³⁰ But if they’re true, we can infer that Dup’s spheres are Cas and Pol, as follows:

(3) Alef and Dup begin with the same facts. ((1), Fact-SV, Qual-G, G-Fix)

(4) Dup begins with [Cas and Pol exist]. ((2), (3))

Assuming (1), it follows by Fact-SV that Alef and Dup begin with the same qualitative facts, and then by Qual-G and G-Fix that they begin with the same facts ((3)). The inference to (4) is straightforward. And (4) precludes new-spheres. So if the A-theorist wishes to take this line, he must reject (1), or (2), or the time version of a thesis on which the inference to (3) depends.

Say that on open-future A-theories, it sometimes isn’t settled what the future will be like in some respects, whereas on closed-future A-theories, it’s always settled what it will be like in every respect (i.e., every time in the world progression fixes every subsequent time).³¹ So if there’s peace now, closed-future-ers say that it was the case earlier that it will be the case that there’s peace. And if there’s now a time block a peace-part of which is present, they say that it was the case earlier that this will be the case. Now, closed-future-ers reject (1). They say that Alef begins with qualitative facts to the effect that two spheres exist and will persist for one second, while Dup begins with ones to the effect that two spheres exist, one of which will persist for one second, the other for two.

This doesn’t mean that closed-future-ers must reject (4), or must resist our CCP at all. But since they reject (1), they can avoid (4) and run new-spheres if they wish. They can say that, were reality to begin with qualitative facts implicating Alef’s qualitative progression, [Cas and Pol exist] would be grounded, but that were qualitative facts implicating Dup’s to hold, the existence of different spheres would be. And closed-future-ers can resist the Time argument in the same sort of way as B-theorists can. On A-theories, we take SS to mean that the initial stretch of fundamental facts in the Alef-progression that would take half a second to elapse is the same as the corresponding stretch in the Bet- and Gimel-progressions. And while the inference to Bet’s and Gimel’s possibility is then natural, closed-future-ers can deny SS. They can say that Alef’s first fundamental facts at least partly (on qualitativist holism, perhaps wholly) differ from the first fundamental facts in any possible nm-duplicate of Bet and Gimel, by foretelling a different future.

Open-future A-theorists, however, can’t avoid (4) by rejecting (1).³² And I’ll now argue that they can’t credibly salvage new-spheres by rejecting (2) or the inference to (3) either. The upshot will be that this line of resistance isn’t open to open-future-ers.

I’ve noted (fn 30) that, though you might reject (2) in virtue of rejecting endurantism, the argument against new-spheres can be sustained with a non-endurantist variant. But suppose our open-future-er rejects (2) in virtue of the thought that, at the Alef-progression’s first time, T, it isn’t (yet) settled which particular spheres exist. Here are two views about the unsettledness:

(Ua) The spheres that exist at T lack thisnesses then.

(Ub) The thisnesses at T are poised between alternatives.

On Ua, T has no determinate non-qualitative facts; on Ub, only disjunctive ones (the difference came up in §3.2). And here are three views about if or when the unsettledness resolves:

(Wa) It doesn’t.

(Wb) At some later time in the Alef-progression.

(Wc) Only from some sort of “timeless” vantage point “external” to the progression.

UaWa is a tantamount to Qual-D (there are no determinate non-qualitative facts), and yields no-factual-difference. UbWa perhaps yields this too if Alef’s spheres’ thisnesses are poised between the same alternatives (cf. §3.3’s bi-location variation). But our open-future-er could try to run new-spheres via Wb or Wc. The idea would be that, if reality progresses after T so as to actualize Alef’s nm-qualitative character, the spheres’ thisnesses resolve into Cas’s and Pol’s, but that if matters progress so as to actualize Dup’s, a different pair of thisnesses.

It’s not clear that Wb can accommodate this idea, since the Alef-progression seems to nm-qualitatively diverge from the Dup-one, not by virtue of any times in the former, but by ending when it does. At which point, it’s too late for the thisnesses to resolve in the progression.³³ This takes us to Wc; perhaps the thisnesses could resolve from an external perspective comprehending the entire progression. But since progressions aren’t real (§5.1), it isn’t clear that progression-external facts (a fortiori, their being qualitatively grounded) are ultimately intelligible. And regardless of the “W” view, I think Ua and Ub founder on the reasoning in §3.2. Suppose T were actual. Given Things, we may say that Det, ∃x∃y(x and y are material spheres a foot apart). In which case, I think it’s compelling that ∃x∃y(Det, x and y are material spheres a foot apart)—contra Ua and Ub.

You might defend Ub’s possibility by appealing to §3.2’s Rep, in which sphere b replaces sphere a, and (I granted) there’s an instant at which the sphere’s thisness is poised between a’s and b’s. Doesn’t this suggest that there could be A-theoretic times whose things’ thisnesses are poised between alternatives? Well, in A-theoretic Rep we get a progression almost every time in which has a sphere with a determinate thisness; there’s just a fuzzy blip in the middle in which the sphere’s thisness is poised between a’s and b’s. But to run no-factual-difference or new-spheres, Ub-ers say that such fuzziness suffuses the Alef-progression, either totally (on Wa and Wc) or until the tail end (Wb). It’s not clear that we can squeeze the credibility of this out of Rep. And even if such indeterminacy could be made credible, running new-spheres requires Ub-ers to address the two challenges raised above for Wb and Wc respectively.

I conclude that open-future-ers can’t credibly salvage new-spheres by rejecting (2). As for the inference to (3), it turned on §5.1’s time versions of Fact-SV, Qual-G, and G-Fix. So suppose our open-future-er claims that a fact in one time can be grounded in or fixed by facts some of which are from (or about)³⁴ another. Specifically, suppose T were actual, that Cas and Pol now exist ((2)), and that he claims that their existence is partly fixed by nm-qualitative facts from or about times in the Alef-progression that differentiate it from the Dup-one. Further, their present existence depends on those partial fixers, in that if matters were to progress so as to actualize Dup’s nm-qualitative character, Cas and Pol wouldn’t exist now. This is new-spheres.

Since progressions aren’t real, it isn’t clear that this sort of diachronic grounding or fixing (in which a fact from one time is partly grounded in or fixed by facts from or about another) is ultimately intelligible.³⁵ But for present purposes, I need only note that the above proposal isn’t open to open-future-ers. Grant that Cas and Pol wouldn’t exist now if matters were to progress so as to actualize Dup’s nm-qualitative character. Since they do exist now, it’s now settled that matters won’t progress in that way, which contradicts our open-future-er’s open-future-ism. If it’s already settled that Dup’s nm-qualitative character won’t actualize, he can avoid (4) by rejecting (1).

Presentists may accept a closed or open future; I won’t get into which they should accept, but just note that new-spheres isn’t open to open-future-ers. While growing-block-ism is consistent with closed-future-ism, open-future-ism has been critical to its motivation,³⁶ and so this line presumably isn’t for growing-block-ers. It seems natural for spotlight-ers to accept closed-future-ism, and hence that they can take this line. However, spotlight-ism is arguably consistent with open-future-ism too.³⁷ Note also that, for new-spheres to be effective, it isn’t enough for B-theorists or closed-future A-theorists to say that their theory is contingently true.³⁸ If there’s a possible open-future variant of Alef, we can base our CCP on it and close off new-spheres.

5.4. Time and Diachronic-Modal-Asymmetry

So open-future A-theorists can’t resist our CCP via new-spheres. Further, I don’t think they can credibly run diachronic-modal-asymmetry either.

On B-theory Qual-G, imagine Alef’s actualizing via the actualizing of a qualitative temporal spread, which then grounds the distribution of particular thisnesses across the spread’s things. Turning now to Dup, we “wipe” this entire spread and “start over” (recall §5.2’s holism): We get a new qualitative spread, which grounds the distribution of particular thisnesses. On new-spheres, we get new thisnesses. On diachronic-modal-asymmetry, the same ones as before. I already criticized this line in §4.2; what I want to add now is that it’s even harder to accept on open-future-ism.

So suppose now that our (would-be) Qual-G-er is an open-future-er. Because possible worlds are progressions, they’re actualized progressively, by adding new times to already actualized ones. And because of the open-future-ism, some progressions—such as Alef and Dup—literally overlap, being numerically the same for some stretch. So suppose their shared beginning (T) were actual: Cas and Pol exist, a foot apart. To run diachronic-modal-asymmetry, our open-future-er says that one of them is such that, were matters to progress so as to actualize Dup’s nm-qualitative character, the longer-lasting sphere would necessarily be it.

This is hard to accept. Let Cas be the possibly-longer-lasting one, and imagine God’s seeing Cas and Pol in T. Because Cas’s and Pol’s thisnesses are already instantiated, it’s hard to believe that he couldn’t add to T by smiting Cas and making Pol the longer-lasting sphere.³⁹ The B-theorist Qual-G-er isn’t in the same position. Consider a short B-theoretic world, W, corresponding to our open-future-er’s T, and suppose W’s qualitative spread tenselessly grounds the distribution of Cas’s and Pol’s thisnesses. Had God wanted to make one sphere outlive the other, he couldn’t have done so by adding to W. Rather, he would have made a different qualitative spread (intuitively, we wipe the W-spread), which would have grounded the distribution of thisnesses. And God wouldn’t even see Cas (qua being Cas) until “after” the spread is there and Cas’s thisness has gone to the longer-lasting sphere.

No doubt more could be said to elucidate why diachronic-modal-asymmetry is less credible on open-future-ism, but I think I’ve said enough to conclude that it is. I also think §4.1’s added indeterminacy is less credible on open-future-ism, but won’t elaborate.

7.1. Costs

I said (§1) I’d argue that various lines all have significant costs, and that we’d see that the prospects for resistance are heavily sensitive to broader metaphysical considerations. We’ve indeed seen that many costs take the form “line L is credible only if you ϕ,” where ϕ-ing is accepting or rejecting some view about ontology, time, or causation. Since these areas partly constitute our metaphysical framework, we may think of ϕ costs as framework costs.

No-factual-difference’s prospects heavily depend on considerations of ontology (§3). For this line is credible only if you reject Things, and the best version (I think), the Qual-D-based one, is credible only if you reject clause T₁ in particular, i.e., deny that material things determinately exist. Assuming Things, would-be Qual-G-ers have new-spheres and the two modal-asymmetry lines to consider. And we’ve seen that the prospects for resistance are heavily sensitive to considerations about time and causation (§§5–6). For new-spheres and diachronic-modal-asymmetry are each credible only if you reject both the open-future A-theory and fundamental spatially scattered local chancy powers. At any rate, I’ve argued that, on either view, new-spheres isn’t available and diachronic-modal-asymmetry strains credulity. Further, these lines’ prospects are also sensitive to considerations of ontology, since some sort of monism might be advanced either to undergird an amenable view about causation or to alleviate some of diachronic-modal-asymmetry’s problems.

ϕ costs aren’t necessarily objections, but will be for anyone who objects to ϕ-ing, and can be extended into objections by arguing against ϕ-ing. For example, the fact that new-spheres is credible only if you reject fundamental spatially scattered local chancy powers will constitute an objection to that line for anyone drawn to such powers, and can be extended into an objection by arguing for them. Other “costs” are simply direct objections: To accept that the cost is real just is to accept that the relevant line’s plausibility is diminished, though we might haggle over how much. This was my main complaint about the modal-asymmetry lines (§4); there are various respects in which they seem unprincipled, ad hoc, or bizarre. And we’ve yet to consider direct objections to new-spheres.

The most serious direct objection, I think, is that it saddles us with a lot of essentialism about qualitative features. On this line, Alef’s spheres couldn’t exist in Bet’s and Gimel’s qualitative spread, since it would ground the existence of different spheres. This might seem objectionable in itself, and may augur additional essentialism. For on perhaps the most natural (or dialectically stable) way of filling out Cas’s and Pol’s modal profiles, Cas and Pol couldn’t exist in any other qualitative spread. And if we generalize to other things, we get a putatively Leibnizian outlook on which all possible things have particular qualitative roles essentially.⁴¹ Can we really accept, for example, that if the cup in front of you had been a bit to the left, then the person in your chair wouldn’t have been you?

7.2. What’s Most Reasonable?

Having surveyed costs for our lines of resistance, here are two salient questions:

(Q₁) Which line(s) is (are) most reasonable?

(Q₂) Is it reasonable to resist our CCP?

(The most reasonable line(s) could still be less reasonable than accepting haecceitism.) I can’t (straightforwardly) answer either here, since much depends on the reasonableness of the “ϕs” in the ϕ costs—which I haven’t assessed. For example, since no-factual-difference is credible only if we reject Things (the line’s ϕ price), this line is reasonable only if it’s reasonable to pay this price. Now suppose we also think that this line is reasonable iff it’s reasonable to pay this price, and that we can reasonably resist our CCP, if at all, only via this line. Then we can’t answer Q₁ or Q₂ without assessing Things. Another reason I can’t answer Q₂ here is that much depends on the strength of the case for qualitativism—which I haven’t assessed. If strong enough, resistance could be all-things-considered reasonable even if the line taken faces serious problems. But by identifying ϕ costs and direct objections, my argument can help you answer Q₁ and Q₂.

Let me briefly discuss the above direct objection to new-spheres, and then (even more briefly) how it compares to the modal-asymmetry lines’ direct objections. This objection seems to turn on de re modal intuitions: It seems to many of us that material things have many of their qualitative features accidentally. For instance, when we consider Alef, it seems that (S₁) those very spheres (not merely similar ones) could have originated an extra foot apart, or that (S₂) each of them could have existed for an extra second. Now recall (§1) that I’ve been trying, not to persuade sanguine haecceitists to reject haecceitism, but to ascertain whether would-be qualitativists can reasonably do so. And of the three routes to qualitativism noted in §1 (which I don’t claim are exhaustive), the first two are informed by scientific virtues or practice, and those drawn to these routes may not give much weight to de re modal intuition. And while those drawn to the third may give weight to this sort of intuition, they’ll either lack the specific ones undergirding the objection or have competing, anti-haecceitist intuitions to consider.

Further, considerations about time and causation may affect what intuitions you have, or how strongly you have them, or their epistemic force. Suppose you feel S₂ strongly. And suppose you accept a time-causation package that permits new-spheres; for instance, B-theory Humeanism. It’s often said that the A-theory, or a specific A-theory (such as presentism), is the common sense view.⁴² Fundamental local cross-time causation (the bit of reality over there produces the next bit over there) also seems part of common sense. And it’s plausible that intuitions about cross-time matters are shaped by common sense views about time or causation. So, your intuitions about cross-time matters (e.g., S₂) may be shaped by a perspective about time or causation that you reject, which compromises their epistemic force. And self-consciously thinking about modal reality from a B-theoretic Humean perspective may diminish their psychological force. S₁ may provide a helpful diagnostic. If you feel it just as strongly as S₂, then S₂’s force (psychological or epistemic) may trace to that of a more general conviction in accidental qualitative features, and so not be shaken by time-causation considerations in particular.

I tend to find the modal-asymmetry lines’ direct objections more damaging than new-spheres’s. First, I think any version of qualitativism must swallow a hefty dose of qualitative essentialism, and so must bite bullets vis-à-vis anti-essentialist intuitions. (I’m talking about our account of sober metaphysical truth. No doubt qualitativists may adopt conventions that let them say that things have all sorts of properties accidentally.) On Qual-D, there are no determinate facts about particular things at all, a fortiori none to the effect that any particular thing could have existed with different features. And even synchronic-modal-asymmetry induces some essentialism about spatially extrinsic matters. Presumably the modal-asymmetry lines induce less essentialism than new-spheres. But because of the former lines’ oddities, it’s hard to know how much. This leads to my second point. For reasons already noted, would-be qualitativists should already be prepared to withstand anti-essentialist intuitions. The modal-asymmetry lines’ problems, by contrast, don’t seem to be ones would-be qualitativists should have expected to confront.

7.3. Must Qualitativists Resist?

Since I suspect that many who are sympathetic to the case for qualitativism will nevertheless find it unreasonable to resist our CCP, it’s worth briefly revisiting whether qualitativists must resist it. We’ve been assuming that qualitativism is to be understood via Qual-G or -D, the accounts on offer in the literature. In which case, qualitativists must resist.⁴³ But I think there should be another possible account of qualitativism, or at least a thesis close to it, that’s consistent with haecceitism.

I noted (§2) that we can distinguish kinds of haecceitism, that differ over the extent of GCPs. So we can consider more rampant haecceitisms, on which pretty much any thing in any possible world can be ripped from its qualitative role without compromising possibility, and more reserved haecceitisms, such as kinds on which the only GCPs are symmetry-breaking ones. And I think, first, that there should be a principled stance that accepts only symmetry-breaking GCPs. For I agree with Melia (1999) that these CCPs differ from others in threatening physical determinism, which suggests that the underlying metaphysical mechanics differ between these CCPs and others. And since modal stances are plausibly underpinned by non-modal ones (e.g., ones about grounding, essence, etc.), I think, second, that there should be a non-modal thesis in the vicinity of qualitativism that underpins such a reserved haecceitism. But that’s a matter for another time.