It is a widespread practice in philosophy to argue for the possibility of p by conceiving/imagining a scenario that verifies p. Stephen Yablo even contends: ‘if there is a seriously alternative basis for possibility theses, philosophers have not discovered it’ (1993, 2). Yet arguments from conceiving/imagining must be handled with care. This can be illustrated by one of the most conspicuous examples to have emerged in recent years. I shall discuss the promises and pitfalls of conceiving/imagining-based arguments for the metaphysical possibility of junk (there are proper parts forming wholes without a mereological sum that is not a proper part itself).

I add a terminological qualification: while the relationship between ‘conceiving’ and ‘imagining’ needs to be clarified, the authors in the debate sometimes speak of conceiving and sometimes of imagining junk without specifying the distinct operations they have in mind.Footnote 1 A use of conceiving and imagining as in the junk-debate requires us to think of them in more holistic terms, involving whatever it takes to represent a scenario in the right way. I shall abbreviate the cumbersome talk of conceiving or imagining by ‘c/imagining’ to refer to the relevant combination of conceiving and imagining.

I shall motivate why I proceed by a case study on c/imagining junk notwithstanding the lengthy debate on zombie-cases and the like and the many alternatives for modal epistemology to have emerged recently (an exemplary list in Vaidya & Wallner, 2021, S1910). My case study brings to the fore one main reason why c/imagining-based epistemology is still relevant. As perfectly illustrated by the debate on junk, philosophers for the better or worse do use c/imagining as a guide to modal knowledge. I explore evidence that can be obtained from the practice of philosophers. The c/imagining-based argument for junk is uniquely interesting as a case study in combining the following traits: (i) It was ground-breaking in putting a new and far-fetched possibility on the table. (ii) It is mostly accepted (contrary to zombies etc.) by the participants in the relevant debate and therefore shows how relevant the use of c/imagining is to modal epistemology. (iii) It displays two typical key features of c/imagining-based arguments: structural isomorphy with the target possibility, and the need for relevant concretion. (iv) One particular lacuna with regard to both features can be pinpointed so as to bring out a characteristic danger of moderate modal illusion: our positive c/imagination of junk does not yet include a sufficiently developed metaphysical understanding of what it takes for there to be a plenitude of proper parts forming wholes without an all-encompassing sum.

I summarize the discussion to come. (1.) I outline a concern about the debate on junk. The most influential scenario is not guaranteed to be junk. This raises a concern of moderate modal illusion: the c/imagining of something that is not yet junk is used to argue for the possibility of junk. (2.)–(2.1.) I distinguish uses of c/imagining that are clearly insufficient from positive uses that might do better. (2.2.) Positive c/imagining sometimes proceeds by building a structural facsimile of a target possibility. In the case of junk, the facsimile covers part of the required structure. (2.3.) Positive c/imagining has to be relevantly concrete. (2.4.) It has to integrate knowledge from other sources. Extant knowledge in the case of junk leaves relevant issues unanswered. (2.5.) Such an integration gives rise to a combinatorial perspective on metaphysics first- and theory-based alternatives. (3.) I elaborate the resulting risk of a moderate modal illusion: our positive c/imagining covers some aspects of junk by a structural isomorphy. It is supplemented by a clause that is not yet fully grasped with regard to its metaphysical implications.

1 A concern about the debate on the conceivability of junk

Einar Duenger Bohn made a famous case for the (metaphysical) possibility of junk-worlds. Bohn defines a junk-world w: w is junk iff anything in w is a proper part. Bohn argues for the possibility of junk-worlds by c/imagining two worlds:

‘[w1] Everything in this world is spatially extended and just one half of something else that is also spatially extended. That is, for any thing in this world, there is something else of which it is a spatial proper part. … [w2] Our universe is a miniature replica universe housed in a particle of a bigger replica universe, which is again a miniature replica universe housed in a particle of an even bigger replica universe, and so on ad infinitum.’ (2009b, p. 28, see Parsons, 2007; Schaffer, 2010, p. 65).

w1: for every x in w1, x is spatially extended and there is a y in w1 such that x is one half of y.

w2: there is an infinite series of universes, each of which is a proper part of some other universe.

There is a problem with Bohn’s argument. The limited description of w2 can be consistently interpreted in two ways (Watson, 2010):

w2j: there is an infinite series of universes, each of which is a proper part of some other … and there is no mereological sum of all the universes in the series which is not a proper part of any other.

w2nj: there is an infinite series of universes, each of which is a proper part of some other … and there is a mereological sum of all the universes that is not a proper part of any other.

Bohn (2010, 296–297) clarifies his argument for junk: three separate premises together provide good albeit defeasible evidence for the possibility of a junk-world:

(Conceivability)Footnote 2 ‘…junky worlds are (positively) conceivable…’.

(Consistency) ‘…junky worlds are logically consistent (in the sense of there being mereological models of them involving no controversial mereological principles)…’.

(Advocacy) ‘…their possibility has been defended by such serious thinkers as Leibniz and Whitehead…’.

These clarifications mark the ultimate step in the development of Bohn’s argument for junk. The c/imagining-based argument proved much more effective in shaping the subsequent debate than Bohn’s earlier general Humean argument against necessary connections that would ensure a fusion to exist for any set of objects (2009a). Still there are doubts even about the c/imagination-based argument: first, the success of the argument crucially depends on (Conceivability). Second, the role of w2 raises the salient alternative that the acceptance of (Conceivability) rests on a modal illusion even concerning w1.

The locus classicus on modal illusion is Kripke (1980). One takes some p to be possible that is in fact impossible because one mistakes one’s c/imagination of some p* (p* ≠ p) that is closely related to p for a c/imagination of p. In the following, I want to use a somewhat weaker notion of modal illusion that does not involve a false modal belief but only an insufficiently justified modal belief. A subject S succumbs to a moderate modal illusion with regard to p if:

(i) S believes that p is possible.

(ii) S does so only because S has positively c/imagined some closely related p* (p* ≠ p) instead of p.

I formulate only a sufficient condition as there may be other ways to succumb to a moderate modal illusion.

Picking up ‘(positively) conceivable’ from Bohn’s (Conceivability), I distinguish positive c/imagining from easy c/imagining. The former may bear on possibility, the latter does not. There is a risk that one takes junk-worlds to be possible just because one has positively c/imagined w2-worlds without a sufficient understanding of the additional requirements for junk (w2j). This is confirmed by the prominence of w2-scenarios described in a way that does not guarantee them to be junk in the subsequent debate. Some authors simply describe w2-worlds as junky (Cotnoir, 2014, p. 650, Giberman, 2015, p. 439, Morganti, 2009, pp. 280–281,). The same concern arises for scenarios of infinitely tall ordinary objects like ‘junky spruces’ or ‘junky skyscrapers’ as long as we are not told how the mereological structure of ordinary objects like spruces and skyscrapers is reconcilable with being junky (Giberman, 2015, p. 439, 2021, 5651). The diagnosis of modal illusion has already been suggested for gunk (Williams, 2006).Footnote 3 It remains to be developed for junk (see Tallant, 2013, p. 433).

Having raised concerns about the pitfalls of positive c/imagining in the junk debate, I shall use Sect. (2) to say a bit more about the relevance and requirements of positive c/imagining. In Sect. (3), I shall then specify my epistemological concerns about the junk debate in light of my considerations on positive c/imagining.

2 Requirements of positive C/imagining

2.1 Easy C/imagining and the need of elaboration

Proponents of c/imagining-based modal epistemology often stress that it takes more to establish that p is possible than merely to c/imagine that p. For instance, Chalmers (2002) distinguishes negative and positive c/imagining. p is negatively conceivable if one cannot rule out a priori that p. Negative conceivability may be tentatively identified with (Consistency). Positive c/imagining requires more than just giving a consistent description. In a similar vein, I oppose positive to easy c/imagining. The latter can be illustrated by examples from the philosophy of imagination (Currie & Ravenscroft, 2002; Kung, 2016). Philosophers have emphasized that imagination per se is not restricted by possibility, not even by consistency. For instance, one may conjure up imagery as of a woman in nineteenth century attire with a description: Ada Lovelace, having just shown that Goedel’s Theorem is false. One thereby imagines that Goedel’s Theorem is false. Having imagined Goedel’s Theorem to be false, one can do the same with other metaphysical and even logical necessities. What is lacking are the crucial details of the imagined proof.

Transferred to Bohn’s argument, positive c/imagining has to give us a sufficient grip on what it takes for something to be junk. In the next Sects. (2.2–2.5) I shall outline some resources from the discussion on Bohn’s argument.

2.2 Structural isomorphy

I suggest that often positive c/imagining works by a limited structural isomorphy with its target scenario. A view along these lines has been advocated by Ichikawa and Jarvis:

‘Considering a fleshed out scenario raises the likelihood of finding absurdities that might otherwise have escaped one’s notice. The most straightforward way to flesh out a scenario is mentally to construct a structural facsimile of it. Structural mental representation (as opposed to linguistic or conceptual representation) is most familiar from the process of visualization. Offline perceptual simulations can be used to structurally represent spatial relations—but they might also be used to represent other sorts of relations as well, just as a visual graph can model the change in population of India over the last fifty years.’ (Ichikawa & Jarvis, 2012, p. 151).

Ichikawa and Jarvis argue that structurally representing a scenario makes it easier to detect hidden conceptual contradictions in the scenario. Unfortunately, a huge gap remains between their example of a visual graph representing population changes and the purported role of structural representations in detecting absurdities and judging modal issues more generally.

Looking at Bohn’s w2-scenario helps to close this gap. This may also explain why w2 plays a larger role in the debate after Bohn than the (unambiguously junky) w1-scenario. It provides an example of how we address whether junk is possible by building a representation that displays a structural isomorphy to a junk-scenario. The structural isomorphy is very limited, though. Our representations themselves do not have to be mereologically structured. Yet they display an algorithmic structure: begin with representing a universe, then represent a universe of which the first universe is a proper part, and so on. The ascent from representing a universe to representing more comprehensive ones without end follows the being part of-relation among infinitely many universes.

This isomorphy is no accident. It gives us a better grasp of the make-up of junk- scenarios. I discern two challenges for a junk-scenario. Bohn’s c/imagination of an infinity of nested universes answers to the first but not yet to the second. As for the first challenge, for something to be a proper part, there has to be a corresponding whole. When we encounter the idea of a structure in which everything is a proper part, it is natural to wonder where the wholes are that complement all these parts. The scenario of an infinity of nested universes provides a solution: take any part. The repetitive structure gives you a whole of which it is a part. In ascending from any given universe to a larger one, we become aware that there is a whole for any of these universes to be part of. In performing the ascent, we become aware that we can go on without end. It is easier to represent an infinity of nested universes by performing such an ascent than to think of them in the abstract.

There remains a second challenge, though, which is not yet addressed by the infinite ascent. How are we to ensure that there is no ultimate all-compassing whole over and above the infinitely many universes that are proper parts? There is not yet a structural isomorphy in our imagination of w2 that would take care of this issue. In the next sections, I shall discuss further features that may distinguish positive c/imagining so as to take care of the remaining challenge.

2.3 Relevant concretion

Further guidance towards the requirements of positive c/imagining can be taken from van Inwagen’s moderately sceptical discussion of conceivability evidence. Van Inwagen is sceptical about knowing far-fetched possibility claims like I could have existed unembodied. He incurs no commitment to a sufficient condition of modal knowledge. Van Inwagen responds to the danger of trivialization involved in easy c/imaginings like the Lovelace-Goedel scenario. His response transpires from two examples (van Inwagen, 1998, pp. 78–79): could there be a naturally purple cow? Could there be transparent iron? The main purpose of these non-philosophical examples is to illustrate the following claim: in order to c/imagine a world verifying p in a way that bears on the possibility of p, one has to c/imagine a way for p to be made true at a suitable level of details. In order to use c/imagination to settle whether there could be a naturally purple cow, one would have to tell how the gene for purple colour becomes inserted into the DNA of a cow by a natural process like mutation and evolutionary selection. The minutes of transparent iron would have to be explicated at the subatomic level. Generalizing from van Inwagen’s examples, positive c/imagination requires one to develop a scenario in relevant details. However, van Inwagen does not tell how the requirement of specifying relevant details can be transferred from his non-philosophical examples to more philosophical ones. The case of junk provides an ideal case for studying such a transfer.

2.4 Integrating imagining and theory

I have outlined two distinguishing features of positive c/imagining. (2.2.) Positive c/imagining often works by a limited structural isomorphy with the target possibility. (2.3.) For a p-scenario to justify a judgement of possibility, it needs to be relevantly detailed. I shall now elaborate on the latter requirement. My elaboration nourishes doubts that crucial details are missing in extant c/imagining-based arguments for junk. One would have to provide a non-gerrymandered way of distinguishing when things do and when they do not form a whole that supports junk, or at least tell why an arbitrary-looking distinction will do.

In Sect. (2.2), I have considered the structurally isomorphic representation of an infinity of nested spatiotemporal universes. The minimalistic scenario gives us a solution where the corresponding wholes are if everything is a proper part. However, it does not yet meet a second challenge: it has to be ensured that there is no sum of all the parts. One has to say more on what determines whether there is or there is no sum of given concrete parts, and how these determinants work together in a junk-scenario. I shall explore several exemplary resources for such considerations.

One principled option for filling the gap are meta-metaphysical considerations on how metaphysical questions are decided. An exemplary meta-metaphysical hypothesis is that convention settles mereological questions like whether concrete parts are to form an ultimate sum (Hirsch, 2011; Sidelle, 2009). A conventionalist may embed her exercise of c/imagining into her argument on why mereological structure is settled by convention. Yet there surely are limits on conventions. A conventionalist would have to take stance on the following requirement: conventions should not be arbitrarily gerrymandered but attuned to the theoretical role of mereological relationships.

Another option is to go into the metaphysics of mereology. One relevant debate revolves around van Inwagen’s (1990) special composition question: what are the individually necessary and jointly sufficient conditions for items to compose a whole? A range of limited principles of composition have been proposed explicitly in order to make room for junk and are sometimes supposed to answer the special composition question:

Finite Composition (Bohn, 2009a): Only finitely many things compose.

Weak Mereological Universalism (Cotnoir, 2014; Smith, 2019): Any two things compose a sum.

Cardinal Composition (Vogt and Werner forthcoming): ‘The xx compose an object iff the xx are pairwise non-overlapping and of cardinality smaller than κ.’ κ is a particular regular infinite cardinal.

The main rationale of these proposals is not that they are intrinsically plausible but that they make room for junk, building on the presumed success of Bohn’s argument. They may give rise to a consistent mereology, but they look arbitrary unless we already accept that junk is possible. The metaphysical considerations would have to address this worry. Weird gerrymandered principles may not strike us as obviously impossible (see Bohn, 2009a, p. 197), but they do not clearly seem possible either. We miss an explanation of why in w2j composition is unlimited except for the ultimate fusion.

A third option is to focus on how to understand metaphysical possibility. In his (2009a, p. 196), Bohn generalizes a Humean argument against necessary connections. Objects which exist independently of each other do not necessarily form a whole. However, further argument would be required to establish that Humeanism supports the contingency of composition. Lewis (1986, p. 211) would have denied this. Universalist Humeans may say that wholes are cheap: for any plurality of things, forming a whole is not a connection like causality. It takes no metaphysical glue to tie them together. Things are just there, and that makes a whole. Yet even if we grant the contingency of composition, it does not follow that any principle of composition is admissible. A more limited consequence of Humeanism would be to accept only natural (non-gerrymandered) principles of composition. For instance, in some world, any fusion is permitted, in another world, there are only atoms.

One may further characterize metaphysical possibility by general principles like plenitude (Bricker, 1991): there should be no arbitrary gaps in the space of possibilities. Standard cases of arbitrary gaps arise within a natural series. There appears to be an arbitrary gap in a series 1, 2, 3, 4, 6. Yet it is not obvious how to apply this idea to the question of junk. It may seem arbitrary to demand that the infinitely many universes must form an ultimate sum: ‘(Why would it have to be there anyway?)’ (Bohn, 2010, p. 298). But it may as well seem an arbitrary gap if the universes are there, each being a proper part of some other, but their sum is not there. One may argue that plenitude supports any consistent mereology, however gerrymandered. Yet it is not obvious that multiplying gerrymandered criteria aligns well with the motivation of avoiding arbitrary gaps. Again a more limited consequence of plenitude would be to accept only non-gerrymandered principles of composition.

A fourth option would be to engage with the metaphysics of possible worlds. It is common to characterize metaphysical possibilities in terms of possible worlds, as in Bohn’s argument. How are we to conceive of possible worlds? Instead of trying to generally address the notion of a possible world, I shall make an illustrative use of one particular controversy on junk and possible worlds.

One natural starting point for approaching worlds qua metaphysical possibilities is to think of them not just as coherent formal objects but as ways for a reality of concrete objects to be. In this vein, philosophers like Lewis (1986) and Schaffer (2010) insist that possible worlds are causally closed spatiotemporal universes somewhat like the actual one. Schaffer used this commitment in his argument against junk:

‘No world—provided that worlds are understood as possible concrete cosmoi—could contain worldless junk because a world that contained junk would be an entity not a proper part of another entity at that world. A world would top-off the junk.’ (Schaffer, 2010, p. 65).

Schaffer argues that there can be no junk-world; such a world, understood as a concrete universe, would have to be the ultimate sum that is supposed not to exist. Cotnoir interprets Schaffer as incurring a commitment to the inconceivability of junk (Cotnoir, 2014, p. 150).

If possibilities are to be embedded in worlds, we would need to tell more as to how junky objects are supported by a possible world without that world furnishing the ultimate sum. The corresponding conception of possible worlds would have to come with a different mereology than Schaffer’s while still delimiting a plausible boundary for metaphysical possibility. If possibilities are not to be so embedded, we would need to tell more as to how worldless junk stands alone as a concrete entity of the sort addressed in metaphysics.

A first stab towards a junk-friendly conception of worlds is Bohn’s response to Schaffer:

‘Why cannot the semantics of ‘junky world’ be ultimately cashed in terms of sets: ‘world w is junky’ is true iff w is a member of the set of all sets whose members are such that each one of them is a proper part of some other member of that set? That is, why cannot ‘world’ (and its cognates) refer to a set, and ‘junky’ be a predicate of such sets?… semantics should not dictate ontology. What if some cosmologists claimed tomorrow that the world is infinitely extended and that there exists no universal object comprising it all?’ (Bohn, 2009a, p. 200).

Instead of Schaffer’s conception of a world as a maximal spatiotemporal whole, Bohn suggests to think of a junk-world as a set the members of which are proper parts of other members. Bohn’s argument manifests resources for flexibilizing the notion of a world so as to become hospitable to junk, but it comes at a price. Set-theoretical constructions à la Bohn do not wear their metaphysical possibility on their sleeves. Bohn’s argument may rebut Schaffer’s argument against the possibility of junk, but I doubt that it so far adds sufficient details to positively c/imagining junk.

In sum, c/imagining an infinite series of nested universes seems the most promising starting point for positively c/imagining junk. Yet such a c/imagination still leaves open whether there is or there is not to be an ultimate whole. To close this gap, one would have to provide a non-gerrymandered way of distinguishing when things do and when they do not form a whole, or at least to tell why a gerrymandered way would do.

2.5 A combinatorial perspective

The gist of my critical reconstruction of the c/imagining-based argument for junk is that more theoretical elaboration needs to be added to attain positive c/imagining. This drives me towards opening up c/imagining-based epistemology to alternative approaches. I shall consider two main competitors to have emerged more recently, a ‘metaphysics-first’ (Mallozzi, 2023, p. S1940, discussion in Boardman & Schoonen, 2023) and (what may be dubbed) a ‘theory-first’ approach (Biggs & Wilson, 2021; Fischer, 2015, 2016, 2017). My aim is only to draw some lessons from my case study. These lessons concern the potential of combining several approaches to modal epistemology.

Metaphysics-first approaches: The core idea of metaphysics-first approaches is that modal knowledge can be derived via bridge principles from a preceding metaphysical knowledge. This metaphysical knowledge gives us an idea of the subject matter of questions of metaphysical modality in the first place. The typical realization of metaphysics-first approaches is an essentialist modal metaphysics (Mallozzi, 2021, p. S1939).

There are several lessons to be drawn from the debate on junk on metaphysics-first approaches. As far as I have surveyed the debate, it does not rest on explicit claims about essences. Positive c/imagination of a junk-scenario in combination with (Consistency) and (Advocacy) is supposed to do the main work. The undeniable success of Bohn’s arguments in shaping the metaphysics of mereology supports a positive albeit critical reconstruction rather than a revisionary epistemology. My reconstruction in turn supports a combinatorial view that integrates lessons from a metaphysics-first approach into an c/imagining-based approach. Metaphysical considerations inform and constrain c/imagining to a certain extent. In the Sect. (2.4), I have gestured at the relevant kind of metaphysical considerations.

The metaphysical considerations may include considerations of essence. To give some examples, an explicit inquiry into the essence of a spruce may provide guidance to c/imagining an infinitely tall junky spruce. An inquiry into what it is to be a world may help decide the debate between Schaffer and Bohn. However, it is not so easy to tell to what extent considerations of essence may help decide the key issue whether an infinite system of nested universes can be supplemented by the condition that there be no ultimate whole. Again one may inquire into the nature of a universe, or one may inquire into the nature of parthood, but it it is not a matter of course that an explicit reasoning in terms of essences is the most succinct way of framing the relevant metaphysical inquiry.Footnote 4

I supplement my discussion of a metaphysics first-approach by considering the problem of ‘modal epistemic friction’ (Mallozzi et al., 2023; Vaidya & Wallner, 2023, p. S1914, Sect. 4.1). Vaidya and Wallner maintain that a c/imagined scenario has to be checked for compatibility with the fundamental natures of the things involved before it can be used as evidence for possibility. In order to do so, one has to build on a preceding knowledge of these natures. Vaidya and Wallner make two presuppositions that can be contested. The first is to formulate the requirement of keeping track of the identities of things (and properties, relations etc.) in terms of essence. The move is contestable as far as it presupposes a commitment to essentialist metaphysics of the sort espoused by authors like Fine or Hall (Vaidya & Wallner, 2023, Sect. 7). Second, Vaidya and Wallner presuppose that an independent knowledge of essences would have to precede the exercise of c/imagining. My case study of the use of c/imagining in establishing the possibility of junk suggests otherwise: instead of explicitly invoking a preceding knowledge of essences, the philosophers enmeshed in this debate rely on their capacity of tracking the identities of things throughout the scenarios c/imagined. The closest reconstruction of this practice gives us the following picture: there is a transition from knowledge of actual things to c/imagining them in non-actual situations that bypasses explicitly settling the essences of such things. Dispositions of recognizing actual things that fall under a category extend to more or less close counterfactual situations. As my criticism illustrates, the confident transition to c/imagined scenarios may sometimes lead us astray. Yet doubts about particular instances do not amount to principal doubts about our capacity of performing the transition.

Theory-based approaches: My case study provides evidence for integrating lessons from a metaphysics first-approach into a c/imagination-based approach. The evidence also applies to a theory-based approach. Fischer (2015) proposes to assess modal epistemologies in the same way as abductive hypotheses in general: by their theoretical virtues, especially conservatism and simplicity. According to Fischer (2015, 2016, 2017), the best framework is a theory-based epistemology of modality (TEM). Claims to possibility and necessity have to be derived from theories. Yet judging from my case study, c/imagination-based epistemology has advantages both in terms of conservatism and simplicity. A theory-based explanation of our modal knowledge may fare better if we disregard how philosophers actually reason. However, things look different if we take into account the explicit reliance on c/imagining. The simplest and most conservative epistemology that takes into account the way philosophers argue for their modal claims is a c/imagination-based epistemology.Footnote 5 One may doubt that such an epistemology integrates well with the epistemology of other fields of inquiry, in particular science. Such doubts can be assuaged by pointing to the need of integrating cognitive activities of simulation in e.g. mindreading and science. It seems likely that the epistemology of simulation significantly overlaps with a c/imagination-based modal epistemology.

3 The suspicion of modal illusion again

Having discussed the requirements of positive c/imagining, I shall now provide a tentative diagnosis where a failure of positive c/imagining may lead us astray in the actual debate on junk. Extant conceivability arguments are not sufficiently safeguarded against moderate modal illusion. The persistent tendency to present an infinite series of nested objects as a case of junk calls for an explanation.

One tempting explanation goes as follows: w2 is the scenario invoked in the discussion after Bohn (2009b). When we try to c/imagine junk, we primarily imagine a structure as embodied by w2. We do so as described by Bohn: represent our universe, add another universe of which the former universe is a part to your representation and so forth without end. The isomorphy between a junky structure and the ascent from representing the actual to representing ever more comprehensive universes ad infinitum makes us understand how there could be a whole for every part if everything is a part. In this respect, w2 gives us a more thorough understanding than the fully junky w1.

We do not yet have a comparable understanding of the condition that there be no ultimate whole of which everything is a part, but we are willing to add this condition by stipulation, perhaps guided by the partial understanding that is provided by arguments like Bohn’s Humean argument for the contingency of composition (2009a). This gives us.

w2j: there is an infinite series of universes, each of which is a proper part of some other … and there is no mereological sum of all the universes in the series which is not a proper part of any other.

However, I have raised doubts that the consequences of adding the stipulation no ultimate whole are yet fully understood as long as relevant details are not elaborated along the lines indicated in Sect. (2.4). A plausible requirement for such an elaboration is to provide a non-gerrymandered way of distinguishing when things do and when they do not form a whole, or at least to tell why a gerrymandered way would do. Without such an elaboration, one has c/imagined but not yet positively c/imagined w2j. There is a danger that one mistakes the limited positive c/imagination of w2 for a positive c/imagination of w2j and therefore takes junk to be possible. A fortiori the same goes for w1: the clause ‘Everything in this world is spatially extended and just one half of something else’ entails that there is no ultimate whole but does not add a sufficiently comprehensive understanding of that condition. A circularity worry ensues: principles of limited composition tailored to make room for junk are motivated by the positive conceivability of junk, but a positive c/imagining of junk may in turn depend on first telling why such junk-friendly principles of limited composition are legitimate.Footnote 6

4 Summary

I have given a positive but critical reconstruction of the use of c/imagining as evidence for the possibility of junk. The reconstruction on the one hand supports the successful philosophical practice of using c/imagining in establishing junk as a relevant possibility. On the other hand, I have tried to more meticulously articulate the requirements of positive c/imagining, raising concerns about the discrepancy between some of the exercises of c/imagining involved and their purported achievement. My overall aim was to raise our awareness of the potentials and pitfalls of c/imagining-based arguments.Footnote 7