Contribution
Allori borrows functionalism from the philosophy of mind (“the wavefunction is as the wavefunction does”, §3.1) and applies it to the quantum state rather than to space or spacetime. The result is a blended position. It is non-material, like primitive ontology and epistemic views. It is non-epistemic, unlike epistemic views. It is non-representational, like Healey’s pragmatism. And it supports constructive explanation, unlike pragmatism.
Key insight
Treat ψ as one realizer of an ingredient of the law, the way a potential is an equivalence class up to a constant. Then the standard objections to ψ-as-law — that it changes in time and is not unique — lose their grip, because an ingredient of the law may be time-dependent and multiply realizable even if the law itself is neither (§3.4, pp. 15–16).
Assumptions
- A realist framework, and a starting assumption that ψ does not represent anything physical (p. 1, “contra wavefunction realism”).
- Laws are real, or at least nomological content is (objection 4 reply). Talk of an ingredient’s function is taken to be meaningful for laws (objection 3).
- Theories whose laws are written with different realizers but share their content count as the same theory (objection 3, follow-up). This is illustrated by the guidance equation versus the quantum potential, and by the empirical equivalents of Allori et al. (2008).
- Constructive explanation — compositional and dynamical, as in kinetic theory — is preferred to principle explanation (§§2.3–2.4).
- Non-relativistic QM, with primitive ontology as the paradigm case.
Key results
- §2 survey of four views. Wave-function realism faces the configuration-space problem and empirical incoherence. Primitive ontology’s ψ-as-law faces time-dependence (Brown and Wallace 2005) and non-uniqueness (Maudlin, p.c.). Epistemic views face interference and PBR. Healey’s pragmatist quantum realism explains only by principle, giving reasons to expect, not reasons why (§2.4).
- §3.2 three roles. Empirical: ψ is part of the Born-rule machinery, and a phase-shifted ψ or a density matrix would serve (p. 12). Nomological: it governs the primitive ontology, or supplies Healey’s “information bridges” (p. 13). Explanatory: constructive or principle, depending on the framework.
- §3.3. ψ is “an ingredient in the law, rather than a law itself” (the birthday-cake analogy, p. 14). It “partially realizes the law”, is one of several possible realizers, and is not reductionist: realizers are specified over and above the matter distribution (p. 15).
- §3.4 claimed advantages. No uniqueness or time-independence requirement. Objective, hence ontic, hence “does not fall prey of the PBR theorem” (p. 16). Constructive explanation available. Configuration-space and empirical-incoherence problems “never arise” (pp. 16–17).
- §3.5 five objections. (1) Is ψ reduced? No: functionalism is compatible with dualism about realizers. (2) Who needs it? Those who want to “have it all”. (3) What is “part of the law”? One of the possible realizers of functions in the law. (4) How can a non-existent thing explain? The law exists, and ψ carries some of its information. (5) Configuration space re-enters in the law. Allori’s answer: nonlocal nomological facts are less problematic than a material ontology in configuration space, “especially from a Humean perspective” (p. 21).
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | ψ can be defined functionally by empirical, nomological and explanatory roles | moderate | informal argument by analogy with functionalism in the philosophy of mind and of spacetime (§3.1–3.2) |
| C2 | As an ingredient of the law, not a law, ψ may be time-dependent and non-unique | moderate | informal argument by analogy with potentials (§3.4) |
| C3 | Being non-representational but non-epistemic bypasses PBR | weak | assertion (fn. 32, p. 16); PBR’s framework is not engaged |
| C4 | Wave-functionalism supports constructive, not only principle, explanation | weak | the two-slit illustration (p. 16); the constructive story is the primitive ontologist’s, so this is inherited, not new |
| C5 | The configuration-space problem “never arises” | weak | assertion (p. 17), partly withdrawn in the objection 5 reply, where configuration space re-enters through nonlocal nomological facts |
| C6 | Nonlocal law in configuration space is more palatable than material ontology there | weak | informal argument from the directness of perception (p. 21) |
Concepts
- Wave-functionalism: “the wavefunction is whatever functions it plays in the theory” (p. 10).
- Ingredient of the law, or partial realizer: a symbol or variable that encodes part of what a law needs to fulfil its nomological role, as constants and potentials do (p. 14).
- Constructive versus principle theory: Einstein’s (1919) distinction. Constructive theories explain dynamically and compositionally from micro-constituents; principle theories constrain what can happen (p. 7).
- Pragmatic versus pragmatist: a view focused on the macroscopic data, versus one that understands a concept by its functions (fn. 31).
Connections
This is the fullest statement in the record of a non-representational ψ-as-law view. It sits in Chen’s weak nomological cell (LIT-204 §4.2) and is exposed to that survey’s fn. 28 “too cheap” objection. Belot’s (LIT-100) objections to ψ-as-law — time-indexed laws and grades of necessity — are cited (fn. 22) and answered only by the claim that an ingredient of the law may be time-dependent. That concedes Belot’s point that ψ behaves “more like an initial condition”. Allori’s “false dichotomy” claim about ontic and epistemic reaches a conclusion close to Hance et al. (LIT-090): the Harrigan–Spekkens categories are not exhaustive. Hance et al. argue it with a stated condition; Allori does not. Neither changes what PBR (LIT-062) proves inside its framework. Dorato (LIT-176) gives a rival non-material reading (powers of events), and Gao (LIT-121) argues the opposite, ψ-ontic, case. Poltorak (LIT-164 §5.4) uses nomological readings like this one to separate ontic status from causal status.
Metaphysics. The work defends a thesis about the ontological category of ψ, grounded in a realist, and apparently Humean-compatible, view of laws, plus functional realization. The metaphysics tag is justified. The primary tag quantum-foundations is right; philosophy-of-science (explanation) is a fair second.
Bearing on the record
It is a node in the wave-function cluster. It supports no THEORY document. Nothing for ML practice.
Limitations
- The central notion, “part of the law”, is given only by analogy (the cake, potentials). No criterion separates an ingredient of the law from a material posit, which is exactly what the too-cheap objection targets.
- It says nothing about relativistic or field-theoretic settings.
- The PBR bypass is by redefinition.
- The explanatory advantage is inherited from primitive ontology rather than supplied by the functional definition.
- The author concedes (objection 2) that purists of each rival view “may not be moved”.
Open questions
- What non-question-begging criterion makes ψ an ingredient of the law while an EM field is material? Without one, the view generalises to classical fields.
- Is the view stable for a non-Humean, given that fn. 46 grants Lewisians may resist it?
- Does “ontic but non-representational” name a position the ontological-models framework can express?
Corrections to the seeded skim
- The dossier says the view “bypasses the no-go theorems” by making ψ ontic but non-material. The paper’s only argument is fn. 32 (pp. 8–9): the ontic/epistemic distinction is a “false dichotomy”, and being non-representational but non-epistemic “alone allows to bypass the PBR theorem”. PBR (LIT-062) is not engaged in its own ontological-models terms, where the question is whether the ontic state λ fixes ψ. The claim is assertion.
- The paper is inconsistent on whether ψ is nomological. It says we should look for “neither material facts … nor nomological facts” (p. 11), and the conclusion’s item 1 has ψ “non-epistemic … without being … nomological” (p. 21). Yet item 3 is “nomological without being a law” (p. 21), the reply to objection 4 says the view is explanatory because “people were realist about laws, or nomological facts” (p. 20), and the reply to objection 5 posits “non-local nomological facts encoded in, or realized by, the wavefunction” (p. 21). Read charitably, the view is realism about law-content, with ψ as one non-unique representation of it. That is close to Chen’s weak nomological reading, and fn. 46 aligns it with Esfeld’s super-Humeanism and Bhogal and Perry’s Humeanism.
- The dossier asks whether the view escapes Chen’s “too cheap” objection. It does not address it, although it cites Chen (2019). The reply to objection 4 (p. 20) embraces exactly the case Chen treats as a reductio: classical EM fields as bookkeeping devices whose explanatory force belongs to the law.
- The dossier omits §3.4 (pp. 15–17), where the advantages are argued. Also, “wave-function realism is compatible with both” on p. 16 is a slip for wave-functionalism.