Symmetries and Paraparticles as a Motivation for Structuralism
Bibliographic record
Abstract
This article develops an analogy proposed by Stachel between general relativity (GR) and quantum mechanics (QM) as regards permutation invariance. Our main idea is to overcome Pooley's criticism of the analogy by appeal to paraparticles. In GR, the equations are (the solution space is) invariant under diffeomorphisms permuting spacetime points. Similarly, in QM the equations are invariant under particle permutations. Stachel argued that this feature—a theory's ‘not caring which point, or particle, is which’—supported a structuralist ontology. Pooley criticizes this analogy: in QM the (anti-)symmetrization of fermions and bosons implies that each individual state (solution) is fixed by each permutation, while in GR a diffeomorphism yields in general a distinct, albeit isomorphic, solution. We define various versions of structuralism, and go on to formulate Stachel's and Pooley's positions, admittedly in our own terms. We then reply to Pooley. Though he is right about fermions and bosons, QM equally allows more general types of particle symmetry, in which states (vectors, rays, or density operators) are not fixed by all permutations (called ‘paraparticle states’). Thus Stachel's analogy is revived. 1 Introduction2 Structuralism Applied to General Relativity and Quantum Mechanics 2.1 Structuralism and individuality 2.2 The semantics of the structuralist 2.3 General relativity and Leibniz equivalence3 Anti-haecceitism and Quantum Mechanics 3.1 Pure and mixed states; permutations 3.2 Symmetrization and indistinguishability 3.3 Quantum statistics and the bad argument for anti-haecceitism4 The Generalized Hole Argument for Sets 4.1 Models and possible worlds 4.2 Permutations and permutes 4.3 State descriptions and structure descriptions 4.4 Theories; permutability, fixity, and general permutability 4.5 Stachel's argument for structuralism5 Fixed Theories and Metaphysical Under-determination 5.1 Pooley's objection; amending Stachel's premises 5.2 Is SP anti-haecceitistic?6 Superselection and Paraparticles 6.1 Quantum permutability 6.1.1 Symmetry types and symmetric operators 6.1.2 Statistics and symmetrization; superselection 6.1.3 The two arguments for quantum permutability 6.2 Quantum general permutability 6.3 Examples of quantum permutability 6.3.1 Two quantum coins, again 6.3.2 A generalized ray
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.008 | 0.009 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".