Source
Michael Esfeld and Vincent Lam (2008), “Moderate structural realism about space-time”, LIT-895, Synthese 160(1): 27–46, read in full in NOTE-695. Page numbers are the journal’s.
What was actually shown
The position (§1). The “master argument” for intrinsic properties has two premises: relations require relata, and relata “have to be something in themselves”, with intrinsic properties beyond their relations (p. 29). Epistemic structural realism accepts both, radical ontic structural realism rejects both, and moderate structural realism accepts the first and rejects the second (p. 31). “An object as such is nothing but that what bears the relations” (p. 32). The denial concerns fundamental intrinsic properties of basic objects; composites keep theirs (p. 28).
Relations as identity conditions. “Insofar as intrinsic properties account for identity conditions, relations can perform that task as well” (p. 32).
Where nothing discerns. Entangled quantum systems of one kind are indistinguishable and “do not have an identity in time”. Space-time points can stand in the same relations and be numerically distinct, “on certain symmetry assumptions about space-time” (p. 33). For these, “one can simply accept a numerical distinction (diversity) … as primitive”. It tells us “that there is a number of objects that is greater than one … and that is all that it tells us”. It “is not a primitive thisness, for it does not establish an identity in time—or any other sort of an identity” (p. 33). Haecceity is rejected separately, by the hole argument.
No priority (p. 34). Relations cannot be prior, because bundles fail to distinguish entangled systems and symmetric points. Objects cannot be prior, because that “would commit us to primitive thisness”. So neither is.
General relativity (§§2–3). Epistemic structural realism individuates points independently of the metric, and the hole argument punishes that (pp. 35–36). Radical realism faces “What does a space-time relation … relate?” (p. 36). The relata are “space-time points (not bare manifold points!)”, whose “structural identity” the metric fixes (p. 37). In the frame-bundle formulation a section defines the points, and the hole argument cannot even be formulated (pp. 40–41). The view is a non-reductive, “sophisticated” substantivalism (p. 43).
What could have come out otherwise. Indiscernible relata could have forced a choice between thisness and elimination. The paper’s reply is a third option, and whether that option is stable is what remains open.
What this does not say
- That GR requires the view. The formulations “naturally receive” it (p. 41). Leibniz equivalence and Stachel’s bundle reading equally support other positions.
- That the metric fixes which point is which in every space-time. §2 says it “completely determines the structural identity” (p. 37), but §1’s symmetric case is an exception, and the Bergmann–Komar labelling it cites works only “for space-times with no symmetries” and through “explicit breaking of active general covariance” (p. 39). In the familiar exact solutions, primitive diversity does the work.
- That primitive diversity escapes Chakravartty’s dilemma. The paper denies it is an identity. Whether that meets the dilemma is a judgement, not a result (NOTE-695).
- That mass and charge are not intrinsic. The paper never discusses state-independent properties.
- That the no-priority argument is complete. It eliminates bundles and thisness only. Weak discernibility, partial dependence and grounding accounts are not considered.
- That it survives the loss of points. Algebraic GR and quantum gravity are deferred to “a separate paper” (p. 44).
Connections
- Chakravartty’s dilemma (THEORY-034). This paper takes the horn with no intrinsic identity-fixing features. THEORY-034 now counts it, beside Floridi’s view, among the record’s readings of that kind; its title said only Floridi’s until it was corrected for this reading. This account is not linked as its rival, because the two disagree about a census and about whether the reply works, not about one phenomenon.
- The owner’s individuation thesis. NOTE-695 finds that the paper holds the weak version of CLAIM-136, plurality without differentiation, not its strict one, and that it gives the objection CLAIM-134 a reply to meet. Its answer to Newman, that relations are concrete and determinate, is a held instance of the remedy CLAIM-138 describes.
- Leitgeb & Ladyman (LIT-154) accept primitive plurality for mathematical places and withhold it for physics. This paper makes the same move for physics, crediting Pooley (2005 §4).
- Quasi-set theory (THEORY-535) counts entangled systems of one kind by a quasi-cardinal, with no identity. Both count without identifying.
- THEORY-038 (Bain and the category-theoretic case) and THEORY-032 (Yoneda) are the record’s other accounts of whether relations can do without relata.