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arxiv: 1906.09041 · v1 · pith:HVVCYXECnew · submitted 2019-06-21 · 🪐 quant-ph

Indistinguishability and the origins of contextuality in physics

Jos\'e Acacio de Barros , Federico Holik , D\'ecio Krause This is my paper

Pith reviewed 2026-05-25 18:59 UTC · model grok-4.3

classification 🪐 quant-ph
keywords contextualityindistinguishabilityquasi-set theoryquantum ontologymeasurement contextsLeibniz principlequantum foundations
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The pith

Properties describing the same physical quantity in different contexts are indistinguishable, modeled via quasi-set theory for a new quantum ontology.

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

The paper tries to establish a formal way to handle properties in contextual quantum systems by treating properties of the same quantity across different measurement contexts as strongly indistinguishable. It develops this using quasi-set theory to describe collections that violate the principle of identity of indiscernibles. This constructs a new ontology for quantum properties. A reader would care because it provides an alternative foundation for understanding contextuality in quantum mechanics based on indistinguishability.

Core claim

By assuming that properties describing the same physical quantity but belonging to different measurement contexts are indistinguishable in a strong sense, and developing a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibniz's principle of identity of indiscernibles, this allows us to consider a new ontology in order to study properties of quantum systems.

What carries the argument

Quasi-set theory, used to model strong indistinguishability of properties across measurement contexts.

If this is right

  • This provides a formal structure for contextual systems.
  • The new ontology avoids traditional context labels on properties.
  • Contextuality originates from the indistinguishability assumption.
  • Quantum systems can be studied with collections that do not distinguish identical properties.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This approach might suggest revising set-theoretic foundations in quantum mechanics.
  • It could be extended to model other quantum paradoxes involving identity.
  • A testable extension would be applying it to specific theorems like Kochen-Specker to see if it reproduces the results without additional assumptions.

Load-bearing premise

The axioms of quasi-set theory can be directly applied to properties across measurement contexts to capture indistinguishability without reintroducing context-dependence.

What would settle it

A specific calculation or experiment demonstrating that the indistinguishability leads to incorrect predictions for a known contextual quantum system, such as violation of expected probabilities in a Bell test setup.

read the original abstract

In this work we discuss a formal way of dealing with properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This allows us to consider a new ontology in order to study properties of quantum systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes that properties describing the same physical quantity but belonging to different measurement contexts in quantum systems can be treated as indistinguishable in a strong sense. It develops a formal description using quasi-set theory (a framework for collections violating Leibniz's identity of indiscernibles) to construct a new ontology for studying the properties of contextual quantum systems.

Significance. If the central construction holds, the work could provide an alternative ontological route to contextuality that avoids standard set-theoretic assumptions about distinguishable individuals. Credit is due for attempting to ground the approach in an existing non-classical set theory rather than ad-hoc postulates, though the significance is limited by the absence of explicit, context-independent mappings from contextual properties to quasi-set elements.

major comments (2)
  1. [Abstract] Abstract and main development: the claim that strong indistinguishability of same-quantity properties across contexts is captured directly by quasi-set axioms requires an explicit construction showing that the mapping from contextual properties to quasi-set elements (or their quasi-cardinalities) is independent of which collection of contexts is chosen; without this, context-dependence risks being relocated into the formation of the quasi-sets themselves.
  2. [Introduction / main body] The framework rests on quasi-set theory previously developed by co-author Krause; the indistinguishability assumption appears tailored to fit that existing non-standard set theory, so the manuscript must demonstrate that the axioms are applied without circularly presupposing the very contextuality the ontology is meant to explain.
minor comments (2)
  1. Provide concrete examples of how specific contextual properties (e.g., spin components in different bases) are represented as elements of quasi-sets, including any quasi-cardinality calculations.
  2. Clarify notation for the quasi-set operations used and ensure all references to prior quasi-set axioms are explicitly cited.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below, providing clarifications on how quasi-set theory is applied to model the indistinguishability of contextual properties.

read point-by-point responses

  1. Referee: [Abstract] Abstract and main development: the claim that strong indistinguishability of same-quantity properties across contexts is captured directly by quasi-set axioms requires an explicit construction showing that the mapping from contextual properties to quasi-set elements (or their quasi-cardinalities) is independent of which collection of contexts is chosen; without this, context-dependence risks being relocated into the formation of the quasi-sets themselves.

    Authors: The axioms of quasi-set theory encode indistinguishability at the level of the elements themselves via the failure of Leibniz's principle, with quasi-cardinality serving as the sole distinguishing feature. This construction is independent of any particular collection of contexts by design of the theory, as the same quasi-cardinal can be assigned to properties of the same physical quantity regardless of context. We acknowledge that an explicit illustrative mapping would strengthen the presentation and will add a dedicated subsection with a concrete example (e.g., for a Kochen-Specker configuration) showing the context-independent assignment. revision: partial

  2. Referee: [Introduction / main body] The framework rests on quasi-set theory previously developed by co-author Krause; the indistinguishability assumption appears tailored to fit that existing non-standard set theory, so the manuscript must demonstrate that the axioms are applied without circularly presupposing the very contextuality the ontology is meant to explain.

    Authors: Contextuality is taken as an empirical feature of quantum mechanics, arising from the impossibility of non-contextual value assignments as established by theorems such as Kochen-Specker. Quasi-set theory is used only as an ontological tool to represent the resulting indistinguishability of properties; the axioms themselves do not encode or presuppose any specific contextual structure. We will revise the introduction to explicitly separate the physical source of contextuality from the formal modeling framework. revision: partial

Circularity Check

0 steps flagged

No significant circularity; application of quasi-set theory is independent modeling

full rationale

The paper applies quasi-set theory—an existing set-theoretic framework for handling violations of the identity of indiscernibles—to model strong indistinguishability of contextual properties. The abstract presents this as a constructive description rather than a derivation that reduces by construction to its inputs. No equations, self-definitions, or fitted predictions are exhibited. Citation of prior quasi-set work by co-author Krause is standard foundational reference and does not function as the sole load-bearing justification for the ontology; the central move is the application itself, which remains externally falsifiable as a modeling proposal.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests primarily on the applicability of quasi-set theory axioms to quantum properties; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Axioms of quasi-set theory permitting collections of indistinguishable objects that violate Leibniz's principle of identity of indiscernibles
    Invoked to model properties belonging to different measurement contexts as strongly indistinguishable.

pith-pipeline@v0.9.0 · 5610 in / 1204 out tokens · 31756 ms · 2026-05-25T18:59:26.238716+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean absolute_floor_iff_bare_distinguishability echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense... quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz’s principle of identity of indiscernibles

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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