The claim
U54: “Individuated objects exist, but only in so far as they are differentiated by their relata.” A194 restated it: “Objects exist, but they do not possess a primitive identity independently of their structural relationships.” It placed the view “close to the non-eliminative OSR developed by Esfeld and Lam” (LIT-895), on which objects and relations are on the same ontological footing and objects are characterized only by the relations they stand in. The record’s survey reading records Esfeld’s moderate structural realism as “there are objects, but all their properties are relational” (LIT-045, NOTE-038).
The owner wrote “objects” without restriction. This claim is filed for the relata of this line: communicative acts, their tokens and their participants. Nothing in the exchange argues the general version, and A203 §35 itself scopes its ontological thesis to “Communicative acts and other structured phenomena”.
The reading adopted. “Relata” in U54 is read as relations: an object is differentiated by the relations it stands in. The literal reading, differentiated by the things it is related to, needs those things to be individuated first. A194 §5 says as much of its own relational profile: “this expression uses already individuated y’s.”
It uses TERM-040’s split of kind, position and token. The claim is about tokens and positions. The kind is CLAIM-137’s.
Two versions
- Strict, the owner’s wording. A relatum exists as an individual only in so far as its relations differentiate it.
- Weak, the assistant’s. Numerical plurality may outrun differentiation, but nothing intrinsic grounds the plurality. A194 §5: “Two distinct objects can occupy structurally indistinguishable positions without becoming numerically identical.” “Their numerical plurality is real; their distinction is not grounded in independent intrinsic identities.” A198 §3: “Relata are numerically real, while their qualitative identity and role are determined by relational structure.” A203 §2: “It is safer to say that qualitative identity and role are relationally grounded, while numerical plurality need not correspond to a unique structural label.”
The weak version has a held precedent, for mathematics only. Leitgeb and Ladyman’s edgeless two-node graph has two nodes that no relation discerns, not even weakly, and they take the identity and difference of places as primitive and internal to the structure (LIT-154, read in NOTE-133). They explicitly withhold the move for physics.
A194 presented the weak version as the owner’s own (“So your formulation can consistently maintain … Numerical distinctness does not require an intrinsic identifying label”). It is a different thesis. The owner has not chosen, and the objections below bite the two differently.
Why character theory does not carry it
A group character classifies a representation up to isomorphism. It does not individuate the vectors of the representation, nor the isomorphic copies of V inside V ⊕ V, which all have the character χ_V and differ only by how they are embedded (CLAIM-132). A194 §6 says so: “A group character classifies the representation up to equivalence. It does not generally individuate each vector.” So the owner’s character analogy supports the kind claim (CLAIM-137) and not this one. This claim needs another ground, which A194 §5 supplies: positions in a structure, and orbits of its automorphism group.
The Yoneda lemma is no help either way. It fixes an object up to isomorphism among objects the category already has, so it presupposes the relata (THEORY-032). That suits the non-eliminative choice and gives no account of what makes two isomorphic objects two.
What it does not say
- That relations exist without relata. It is non-eliminative.
- That it is a theorem of anything. A194 §8: “our proposed interpretation, not a theorem of character theory”.
- That it holds for physics, or for objects in general. A191 §2: “It does not require accepting OSR as the fundamental ontology of physics.”
- That communicative cases contain relata no relation differentiates. Whether two act tokens can be relationally undifferentiated is open.
It faces two objections. Chakravartty’s dilemma reaches it, and the weak version concedes a non-relational ground of identity (CLAIM-134). And the Newman objection presses on it if its relations are read extensionally (CLAIM-138).
Note of 2026-10-10: Esfeld & Lam read
Esfeld & Lam (LIT-895) were read in full on 2026-10-10 (NOTE-695). The reading corrects two things this entry says about them.
- Esfeld & Lam hold the weak version, not the strict one. Relations provide identity conditions wherever intrinsic properties could. Where nothing discerns the relata, as with entangled quantum systems of one kind and points of a symmetric space-time, “one can simply accept a numerical distinction (diversity) … as primitive” (p. 33). So when A194 §5, A198 §3 and A203 §2 moved from “only in so far as differentiated” to numerical plurality without differentiation, they moved toward the view A194 called “close”, not away from it. The strict version is stronger than anything Esfeld & Lam assert. The summary’s “placed it ‘close to’ Esfeld and Lam … then weakened it” should be read in that light.
- “The weak version has a held precedent, for mathematics only” is no longer true. Esfeld & Lam make the same move for physical objects (pp. 33–34), and they credit it to Pooley (2005). They deny that primitive numerical diversity is a primitive thisness, “for it does not establish an identity in time—or any other sort of an identity” (p. 33). Leitgeb & Ladyman remain the mathematical precedent. Neither text extends the move to communicative acts or persons.
The claim’s own content is unchanged. The owner still has to choose between the two versions.
Note of 2026-10-27: the scope it was filed under
This entry was “filed scoped to communicative acts and their participants” because “Nothing in the exchange argues the general version”. At U6 of the exchange of 2026-10-27 the owner set the record’s ambitions as “extremely abstract and unrestricted”, and directed that CLAIM-151’s scope sentence change (its version 3). This claim’s scope still follows its argument, and no argument for either version in general has been given. What has changed is that the owner’s U54 wording, “objects” without restriction, now has an unrestricted frame to sit in: CLAIM-477, on which an entity is partly fixed by the constraints on its relations. That frame leaves this claim’s question open in general, as A8 §5 said: a specification fixes kinds, and what makes isomorphic realizations two (“histories, dynamical continuity, symmetry breaking, locality, or primitive numerical diversity”) is the choice between this claim’s two versions, still the owner’s. Barad’s view, the most radical neighbour the exchange named, A3 placed with radical relational ontology (“independently individuated substances are not fundamental”); whether it eliminates relata is for a reading of LIT-1647. Whether to restate this claim without a domain is left to the owner. Nothing in it changes.
Later the same day, Jaksland 2024 and Faye and Jaksland 2021 were read (NOTE-1230, NOTE-1220), and both quote Barad 2003, 815: “phenomena are ontologically primitive relations—relations without preexisting relata”. Jaksland calls the view a radical relational holism “since only the relational phenomena are ultimately real” and likens it to priority monism (note 9). So Barad’s view is eliminative of relata at the fundamental level, with objects emergent, and is not this claim’s. The non-eliminative precedent in the same neighbourhood is Bohr on Faye and Jaksland’s reading, whose relational properties are properties of real relata (THEORY-1076).
Note of 2026-10-29: what holds it back
The owner has not chosen between the strict and the weak version, and the
objections bite them differently. CLAIM-134 (Chakravartty’s dilemma, through
THEORY-034) and CLAIM-138 (the Newman objection) are live, Proposed and
unanswered. CLAIM-132 is no longer filed as an objection here: it denies
only that the character analogy supports this claim, which “Why character
theory does not carry it” already says. THEORY-032 moves from the grounds
to corroborated_by (ADR-058), since the Yoneda lemma “is no help either
way”.
Note of 2026-10-30: what holds it back
Rechecked after CLAIM-132’s version 2 (2026-10-30), which swaps the unread LIT-893 for LIT-329 in its grounds and adds a derivation; its bearing here is unchanged. The wait is the same: the owner has not chosen between the strict and the weak version, and CLAIM-134 (Chakravartty’s dilemma) and CLAIM-138 (the Newman objection) are still live, Proposed and unanswered.