Spacetime Emergence and the Fear of Intimacy

Claudio Calosi; Cristian Mariani; Samuel T. Baron

REVIEW 3 major objections 3 minor 6 references

Spacetime Emergence and the Fear of Intimacy

T0 review · 3 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper argues that the Argument from Intimacy against mereological spacetime emergence is best answered by rejecting Somewhere and accepting that spacetime regions are locations without being located.

desk verdict A genuinely novel solution to the Argument from Intimacy—reject Somewhere, keep Inheritance—but the paper's own emergence condition turns out to be trivially satisfied under its solution, and the coherence of 'locations without location' needs more defense. read the letter →

arxiv 2412.01404 v1 pith:4FLX2LGJ submitted 2024-12-02 physics.hist-ph gr-qc

Samuel T. Baron , Claudio Calosi , Cristian Mariani This is my paper · ORCID

classification physics.hist-phgr-qc

keywords spacetimeemergencequantumgravityArgumentfromIntimacymereologylocationsuper-substantivalismregionsinheritanceof

topics Quantum Gravity

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to rescue mereological spacetime emergence, the view that spacetime is composed of non-spatiotemporal parts, from the Argument from Intimacy, which says this view contradicts the principle that wholes inherit locations from their parts. It proposes rejecting Somewhere, the claim that every spacetime region is weakly located somewhere, and accepting Nowhere, the claim that regions are locations but do not themselves have locations. The paper argues that this preserves standard mereology and the Inheritance of Location, and that the two arguments for Somewhere fail once objects are located in spacetime by being located at regions that are mereological parts of spacetime. It then argues that identity versions of super-substantivalism are incompatible with this solution and with emergent spacetime anyway, while priority versions fit naturally.

What carries the argument

The carrier of the argument is the formal distinction between Somewhere and Nowhere, built on exact location $L(x,y)$, weak location defined as $WL(x,y) := \exists z(L(x,z) \wedge O(z,y))$, and spacetime defined as the fusion of all regions, $S := \sigma z(\exists x(R(x) \wedge z=x))$. Inheritance of Location, $(P(x,y) \wedge L(y,z)) \to WL(x,z)$, is kept intact. The key maneuver is that regions can serve as locations and bear spatiotemporal properties by standing in a mereological relation to spacetime rather than a locative one, so rejecting Somewhere does not force one to give up standard mereology or the inheritance of location.

What would settle it

A concrete case where a region's spatiotemporal property, such as its metric relation to another region, cannot be derived from its being a part of the spacetime fusion while it has no locative relation to spacetime would refute the paper's answer to the Spatiotemporal Properties argument.

Watch

Extended reading notes

Core claim

The central claim is that the Argument from Intimacy can be resolved by keeping Mereological Spacetime Emergence and Inheritance of Location while rejecting Somewhere ($R(x) \to \exists y\, WL(x,y)$) and endorsing Nowhere ($R(x) \to \neg\exists y\, WL(x,y)$). On this picture, spacetime regions are spatiotemporal locations, but they do not have spatiotemporal locations themselves. Material objects are located in spacetime by being exactly located at regions that are mereological parts of the fusion that is spacetime, so no locative relation between regions and spacetime is needed; regions also get their spatiotemporal and metric properties by being parthood-wise embedded in spacetime structure. The paper further claims that identity super-substantivalism forces a version of Somewhere and, when combined with emergent spacetime, violates the principle that identical things share all properties, whereas priority super-substantivalism avoids this and is the viable substantivalist option.

Load-bearing premise

The load-bearing premise is that spacetime regions can be locations without being located anywhere, and that being parts of the spacetime structure is enough to give them their spatiotemporal and metric properties.

Editorial extensions

If this is right

A perfectly standard mereology, not a reimagined one, suffices for spacetime emergence, since Inheritance of Location can be preserved.
Identity versions of super-substantivalism should be rejected in the context of spacetime emergence because they require Somewhere and conflict with the non-spatiotemporal character of the fundamental substance.
Priority super-substantivalism, on which material objects are determined by but not identical to spacetime, is the viable substantivalist option and pairs naturally with mereological spacetime emergence.
The choice between Somewhere and Nowhere is metaphysically substantive rather than a mere stipulation, because it determines whether the Argument from Intimacy can be answered while preserving standard mereology.
Spatiotemporal properties of regions can be grounded in parthood within spacetime structure rather than in a locative relation between regions and spacetime.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's generalization to arbitrary E-relations hints that the Nowhere solution does not depend on mereology specifically: any relation that embeds regions into spacetime, such as subsethood or membership in a set-theoretic structure, could carry locations and spatiotemporal properties.
A natural next test is whether the priority super-substantivalism defense extends to relationist or monist accounts of quantum gravity, where the determination relation is less clearly a grounding or constitution relation.
If the Somewhere/Nowhere choice is genuinely substantive, formal theories of location may need to decide between the two on explanatory grounds, which could affect unrelated debates about multilocation and extended simples.
The paper's defense of Inheritance of Location is comparative rather than conclusive; a future argument that being a location requires self-location would reopen the case for Somewhere.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper's central move is to reject Somewhere—the claim that spacetime regions are located somewhere—while keeping Inheritance of Location. That is a genuinely new response to the Argument from Intimacy, and the formal framework they set up is clear and useful. The discussion of super-substantivalism is also a real contribution, especially the point that identity versions clash with spacetime emergence while priority versions fit naturally with their solution.

But there are two soft spots worth naming. First, their statement of Mereological Spacetime Emergence is too weak: because parthood is reflexive, under Nowhere every region is itself a non-spatiotemporal part of itself, so the condition is trivially satisfied. The authors say the weak condition is enough to get the argument going, but it also makes their own solution vacuous in that respect. They need to state the principle with proper parts, which is likely what they intend, but as written it undercuts the claim that standard mereology underwrites substantive emergence.

Second, the coherence of regions as locations without being located is asserted rather than argued for. The response to Baron's Spatiotemporal Properties argument relies on the idea that regions derive metric properties from being parts of spacetime, but no principle of property inheritance is given, and it is unclear why such inheritance stops at regions. The reader's instinct is right: this is the load-bearing point, and it needs more work.

These are fixable issues, not fatal ones. The paper is honest about its assumptions, the engagement with the literature is careful, and the formal derivation is valid. The claim that the Somewhere/Nowhere choice is substantively consequential is supported, even if the conclusion is stated more strongly than is warranted.

This deserves a serious referee. It is a contribution to the spacetime emergence debate that should be engaged with, and I would cite it if I work on this topic. I would bring it to a reading group, though I would flag the reflexivity issue ahead of time.

Referee Report

3 major / 3 minor

Summary. The paper proposes a solution to the Argument from Intimacy against mereological spacetime emergence. After formalizing exact and weak location, parthood, inheritance of location, and a weak condition of mereological spacetime emergence, the authors argue that the inconsistency is best resolved by rejecting Somewhere (R(x) → ∃y WL(x,y)) and accepting Nowhere (R(x) → ¬∃y WL(x,y)), while retaining Inheritance of Location. They then reply to two arguments by Baron in favor of Somewhere, and argue that although identity super-substantivalism recreates the problem through a weakened Somewhere, priority super-substantivalism is compatible with Nowhere and with the proposed solution. The paper concludes that standard mereology is sufficient for spacetime emergence and that identity versions of super-substantivalism should be rejected in the context of spacetime emergence.

Significance. If the central argument were successful, the paper would make a substantive contribution: it would show that a perfectly standard mereology can underwrite spacetime emergence while preserving the Inheritance of Location, and it would sharpen the connection between spacetime emergence and priority super-substantivalism. The paper is clearly written, explicitly formalized, and usefully isolates the Somewhere/Nowhere choice point in the debate. However, the significance is conditional on fixing two load-bearing gaps: the formal definition of Mereological Spacetime Emergence is trivially satisfied under the paper's own assumptions, and the response to the Spatiotemporal Properties argument relies on an unstated and undefended property-inheritance principle.

major comments (3)

[§2, Mereological Spacetime Emergence] The formal definition ∀x(R(x) → ∃y(P(y,x) ∧ ¬SP(y))) is trivial under Nowhere. Since P is reflexive and Nowhere yields ¬SP(x) for every region x, the witness y=x satisfies the existential for every region. Thus the principle does not require any genuine non-spatiotemporal proper parts, and the paper's claim that a perfectly standard mereology can underwrite substantive spacetime emergence is unsupported as stated. The authors should either use proper parthood or add a distinctness condition (e.g., y≠x), and then verify that the Argument from Intimacy and the subsequent discussions still go through.
[§4, Spatiotemporal Properties argument] The reply to Baron's Spatiotemporal Properties argument asserts that a region can have metric or spatiotemporal properties 'simply by virtue of being a part of a larger structure, which has those properties' (p. 14), but no principle of property inheritance from wholes to parts is stated or defended. Without such a principle, the assertion does not answer Baron's argument. Moreover, if parthood transmits spatiotemporal properties, the paper needs to explain why those properties do not also transmit to the non-spatiotemporal parts whose existence is required by Mereological Spacetime Emergence. This is a load-bearing gap in the central solution.
[§5, Super-duper Priority Substantivalism] The claim that Super-duper Priority Substantivalism makes matter come 'for free' with the emergence of spacetime is not argued; it is asserted that because material objects are D-related to substanceQG, no separate mereological account of emergent matter is needed. Since D is characterized only by Tracking (xDy → x >f y) and is otherwise left unspecified, the paper should say which determination relation does the work and why it obviates a mereological account of matter. Without this, the advertised conclusion that priority super-substantivalism is the natural bedfellow of mereological spacetime emergence remains under-supported.

minor comments (3)

[§2, Fusion definitions] The displayed definition of Fφz is ill-formed: the second conjunct should be ∀y(P(y,z) → ∃x(φ(x) ∧ O(x,y))), not ∀y(P(x,z) → ∃x(φ(x) ∧ O(x,y))), since the 'x' in P(x,z) is unbound. The General Fusion Operator on the same page has a similar quantifier stretch that should be corrected for readability.
[§5, Identity Theory] The symbol 'O' is used both for overlap and for the predicate 'being a material object'; in the Identity Theory subsection this creates confusion, e.g., WL-Overlap says WL(x,y) := O(x,y), but the derivation requires O(x) as well. Use a distinct predicate, such as 'Mat(x)', for material objects.
[§5] There are typographical slips in the displayed formulas: 'Identity Super-Substantivalism1' and 'Identity Super-Substantivalism2' contain an extra closing parenthesis, and the text refers to 'Lehmkhul (2018)' where the reference list gives 'Lehmkuhl'. These should be corrected.

Circularity Check

1 steps flagged · score 6.0 of 10

The paper's formal solution is logically valid, but its central positive claim that standard mereology can underwrite spacetime emergence is satisfied only by definition: under Nowhere and reflexive parthood, every region trivially counts as its own non-spatiotemporal part.

self definitional [§2 Preliminaries (definitions of P, SP, Nowhere, Regions are not Spatiotemporal, Mereological Spacetime Emergence); §3 The Argument from Intimacy]
"We assume a parthood relation P that is transitive, reﬂexive, and asymmetric. ... Spatiotemporal Entity: SP (x) := ∃yW L(x, y ) ... Nowhere: R(x) → ¬∃ y(W L(x, y )) ... Regions are not Spatiotemporal : R(x) → ¬ SP (x) ... Mereological Spacetime Emergence : ∀x(R(x) → ∃ y(P yx ∧ ¬ SP (y)))"

Given SP(x) is defined as ∃y WL(x,y), Nowhere entails R(x) → ¬SP(x) for every region. Since P is assumed reflexive, P(x,x) holds, so y = x witnesses the existential in Mereological Spacetime Emergence: each region has itself as a non-spatiotemporal 'part.' The condition that each region has a non-spatiotemporal part is therefore satisfied by construction, without any genuine non-spatiotemporal proper parts. Thus the paper's conclusion that 'a perfectly standard mereology can be used for mereological approaches to spacetime emergence' reduces to the definition of Nowhere plus reflexivity of P; it does not establish substantive composition of spacetime from non-spatiotemporal parts.

full rationale

The core solution to the Argument from Intimacy—rejecting Somewhere while retaining Inheritance of Location—is a non-circular logical point: the inconsistent triad is resolved by denying one conjunct. The responses to Baron's Spatiotemporal Properties and Location of Objects arguments are substantive philosophical moves, and the discussion of priority vs. identity super-substantivalism is argued rather than assumed. Self-citations (Baron 2020, Baron 2021, Le Bihan 2018, Calosi and Dürr 2021) are used as background or as targets and are not load-bearing. However, the paper's own definitions introduce a definitional collapse in the positive emergence claim: because parthood is reflexive and Nowhere makes every region non-spatiotemporal, Mereological Spacetime Emergence is trivially true with y = x. The paper explicitly says the weak condition is sufficient for the argument, but its conclusion that standard mereology suffices for spacetime emergence depends on this condition, and that condition is satisfied by construction rather than by any demonstrated non-spatiotemporal composition. This is a partial, definitional circularity in the paper's central positive claim, not in its negative resolution of the triad.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The paper's central argument rests on a small set of explicit mereological and locative assumptions. No free parameters are fitted. The main burden is the unargued-for coherence of 'Nowhere' and the unspecified D-relation in priority super-substantivalism.

assumptions (6)

domain assumption Parthood is transitive, reflexive, and asymmetric; spacetime regions are a model of classical extensional mereology with unique fusions.
Section 2 states 'We will take spacetime regions to be a model of classical extensional mereology.' The definition of Spacetime as a fusion and all overlap-based arguments depend on this.
domain assumption Exact location L is primitive and its second relatum is always a spacetime region.
Section 2 introduces L and the axiom 'Second Argument Spacetime Region'. The definitions of weak, entire, and pervasive location, and the concept of spatiotemporal entity, all rely on this choice.
domain assumption Mereological Spacetime Emergence: every spacetime region has at least one non-spatiotemporal part.
Section 2 formalizes this as the weak condition that drives the Argument from Intimacy; the paper's solution is conditional on this mereological account of emergence.
domain assumption Inheritance of Location (downward): (P(x,y) ∧ L(y,z)) → WL(x,z).
Section 2 states this principle from Sider and Section 3 defends it as non-negotiable; the paper's solution preserves it rather than rejecting it.
ad hoc to paper Nowhere / No Location for Regions: R(x) → ¬∃y WL(x,y).
This is the proposed solution. It is supported only indirectly by rebutting three arguments for Somewhere; its coherence is the load-bearing metaphysical assumption.
ad hoc to paper Priority super-substantivalism: material objects are D-related to spacetime (and spacetime to substanceQG) with D tracking fundamentality and no identity.
Section 5 introduces this to avoid the revenge argument. The D-relation is left unspecified, and footnote 32 concedes no proof that all such relations avoid inheritance-style problems.

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Cite this review

Pith. "Pith review of Spacetime Emergence and the Fear of Intimacy." pith.science (2026). https://pith.science/paper/4FLX2LGJ

@misc{pith2026241201404,
  author       = {Pith},
  title        = {Pith review of: Spacetime Emergence and the Fear of Intimacy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4FLX2LGJ}},
  note         = {Machine review of arXiv:2412.01404}
}

read the original abstract

We provide a reply to the Argument from Intimacy on behalf of defenders of emergent spacetime in theories of quantum gravity. We argue that if one accepts that spacetime regions are nowhere in the sense that they are locations but do not have locations, then the Argument from Intimacy can be resolved. We go on to consider a problem with this response, namely that it is unavailable to super-substantivalists. We argue that this is right for identity but not priority super-substantivalists. We then suggest that there is no cost for our solution here, since identity versions of super-substantivalism face severe challenges in the context of spacetime emergence and so should be rejected anyway.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages

[6]

Somewhere Together: Location, Parsimony and M ultilocation

“Somewhere Together: Location, Parsimony and M ultilocation.” Erkenntnis. At: https://link.springer.com/article/10.1007/s10670-021-00376-y. Loss, R.,

work page doi:10.1007/s10670-021-00376-y
[2016]

Persistence, Vagueness, and Location

“Persistence, Vagueness, and Location”, Journal of Philosophy , 113: 507–532. Eagle, A., 2019, “Weak Location”, Dialectica, 73(1-2): Fine, K

work page 2019
[2018]

Location and Mereology

“Location and Mereology”, Stanford Encyclope- dia of Philosophy , (Fall 2018 Edition), Edward N. Zalta (ed.), https://plato.stanford.edu/archives/fall2018/entries/location-mereology/. Giordani, A. and Calosi, C

work page 2018
[2021]

Parts of Spacetime

“Parts of Spacetime”, American Philosophical Quarterly , 58 (4): 387-398. Baron, S., Miller, K. and Tallant, J., 2022a. Out of Time; A Philosophical Study of Timeless- ness. Oxford: Oxford University Press. 35Note we are not making the stronger claim that one view entails the ot her; one may still ﬁnd space to be a relationist or a super-substantivalist o...

work page 2022
[2022]

Journal of Philosophical Logic

A General Theory of Location Based on the No- tion of Entire Location. Journal of Philosophical Logic . At: https://link.springer.com/article/10.1007/s10992-021-09641-5. Cotnoir, A. J. and Varzi, A

work page doi:10.1007/s10992-021-09641-5
[2023]

Atoms, coms, syllables and organis ms

“Atoms, coms, syllables and organis ms” Philosophical Studies 180: 1995–2024. Humphreys, P

work page 1995

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [6]

Somewhere Together: Location, Parsimony and M ultilocation

“Somewhere Together: Location, Parsimony and M ultilocation.” Erkenntnis. At: https://link.springer.com/article/10.1007/s10670-021-00376-y. Loss, R.,

work page doi:10.1007/s10670-021-00376-y

[2] [2016]

Persistence, Vagueness, and Location

“Persistence, Vagueness, and Location”, Journal of Philosophy , 113: 507–532. Eagle, A., 2019, “Weak Location”, Dialectica, 73(1-2): Fine, K

work page 2019

[3] [2018]

Location and Mereology

“Location and Mereology”, Stanford Encyclope- dia of Philosophy , (Fall 2018 Edition), Edward N. Zalta (ed.), https://plato.stanford.edu/archives/fall2018/entries/location-mereology/. Giordani, A. and Calosi, C

work page 2018

[4] [2021]

Parts of Spacetime

“Parts of Spacetime”, American Philosophical Quarterly , 58 (4): 387-398. Baron, S., Miller, K. and Tallant, J., 2022a. Out of Time; A Philosophical Study of Timeless- ness. Oxford: Oxford University Press. 35Note we are not making the stronger claim that one view entails the ot her; one may still ﬁnd space to be a relationist or a super-substantivalist o...

work page 2022

[5] [2022]

Journal of Philosophical Logic

A General Theory of Location Based on the No- tion of Entire Location. Journal of Philosophical Logic . At: https://link.springer.com/article/10.1007/s10992-021-09641-5. Cotnoir, A. J. and Varzi, A

work page doi:10.1007/s10992-021-09641-5

[6] [2023]

Atoms, coms, syllables and organis ms

“Atoms, coms, syllables and organis ms” Philosophical Studies 180: 1995–2024. Humphreys, P

work page 1995